text: # Algebra - Simplifying Algebraic Fractions
  
  a - answer    s - solution    v - video
  
  ## Question 1
  
  Simplify
  
  a) $\dfrac{6x}{4}$a s v
  b) $\dfrac{8x}{6}$a s v
  c) $\dfrac{8x}{10}$a s v
  d) $\dfrac{21x^2}{14}$a s v
  e) $\dfrac{46y}{2}$a s v
  f) $\dfrac{9\sqrt{a}}{27}$a s v
  
  ## Question 2
  
  Simplify
  
  a) $\dfrac{15}{10x}$a s v
  b) $\dfrac{40}{30y}$a s v
  c) $\dfrac{16}{4p}$a s v
  d) $\dfrac{48}{20a^3}$a s v
  e) $\dfrac{9}{14h}$a s v
  f) $\dfrac{36}{32m}$a s v
  
  ## Question 3
  
  Simplify
  
  a) $\dfrac{2y}{3y}$a s v
  b) $\dfrac{10x}{4x}$a s v
  c) $\dfrac{15z}{5z}$a s v
  d) $\dfrac{5x^2}{5x^2}$a s v
  e) $\dfrac{2\sqrt{y}}{7\sqrt{y}}$a s v
  f) $\dfrac{48y^5}{36y^5}$a s v
  
  ## Question 4
  
  Simplify
  
  a) $\dfrac{3x^2}{2x}$a s v
  b) $\dfrac{9p^3}{5p}$a s v
  c) $\dfrac{5y^2}{y}$a s v
  d) $\dfrac{16z^5}{12z^2}$a s v
  e) $\dfrac{21q^8}{35q^3}$a s v
  f) $\dfrac{44c^{12}}{20c^{12}}$a s v
  
  ## Question 5
  
  Simplify
  
  a) $\dfrac{4x}{5x^3}$a s v
  b) $\dfrac{8x^2}{6x^5}$a s v
  c) $\dfrac{9v^3}{15v^3}$a s v
  d) $\dfrac{35y^4}{50y^{17}}$a s v
  e) $\dfrac{42a^4}{24a^5}$a s v
  f) $\dfrac{19t^{13}}{3t^{13}}$a s v
  
  ## Question 6
  
  Simplify
  
  a) $\dfrac{2(x+1)}{3(x+1)}$a s v
  b) $\dfrac{18(y-2)}{6(y-2)}$a s v
  c) $\dfrac{22(x^2+4)}{10(x+1)}$a s v
  d) $\dfrac{15(x-1)}{39(x-1)^2}$a s v
  e) $\dfrac{77(2x+3)^3}{44(2x+3)}$a s v
  f) $\dfrac{8(4z^2+5)^8}{11(4z^2+5)^{10}}$a s v
  
  ## Question 7
  
  Simplify
  
  a) $\dfrac{x^2y}{x}$a s v
  b) $\dfrac{4xy^7}{xy^2}$a s v
  c) $\dfrac{20x^4y^2}{15x^3}$a s v
  d) $\dfrac{10a^6}{25a^2b^5}$a s v
  e) $\dfrac{4x(x+5)}{3(x+5)}$a s v
  f) $\dfrac{48h^2(g-3)}{40h}$a s v
  
  ## Question 8
  
  Simplify. Leave answers with positive indices
  
  a) $\dfrac{5x}{x^{-2}y}$a s v
  b) $\dfrac{4y^{-3}}{xy}$a s v
  c) $\dfrac{2x^{-5}y^{-3}}{10x^{-1}y^{-2}}$a s v
  d) $\dfrac{15a^{-2}b^{-5}}{6a^{-6}bc^{-1}}$a s v
  e) $\dfrac{21x^{-3}y^4z}{56x^{-8}y^{-1}z^3}$a s v
  f) $\dfrac{108m^{-9}npq^{-15}}{60m^{-2}n^{-12}p^5}$a s v
  
  ## Question 9
  
  Simplify. Leave answers with positive indices
  
  a) $\dfrac{-4a^2bc}{2ab^2}$a s v
  b) $\dfrac{10xy^3}{-6xyz}$a s v
  c) $\dfrac{-8p^3q^2r}{-20pq^2r^3}$a s v
  d) $\dfrac{45p^{-2}q^4}{25p^7q^{-1}}$a s v
  e) $\dfrac{33c^{-1}d^{-7}e}{-21c^{-1}d^3e^8}$a s v
  f) $\dfrac{-27w^{-3}x^{14}y^{-9}z}{-63w^2x^{-3}z^{15}}$a s v
  
  ## Question 10
  
  Factorise and simplify
  
  a) $\dfrac{6x+4}{4}$a s v
  b) $\dfrac{8p-14}{2}$a s v
  c) $\dfrac{15w+35}{20}$a s v
  d) $\dfrac{21a-30}{12}$a s v
  e) $\dfrac{18a^2-20a}{14a}$a s v
  f) $\dfrac{42g^2-66g^5}{24g^3}$a s v
  
  ## Question 11
  
  Factorise and simplify
  
  a) $\dfrac{4x+8}{6x+12}$a s v
  b) $\dfrac{9x+3}{3x+1}$a s v
  c) $\dfrac{x^2+3x}{2x+6}$a s v
  d) $\dfrac{xy-2y}{4x-8}$a s v
  e) $\dfrac{8x+2y}{20x+5y}$a s v
  f) $\dfrac{4x^2+20x}{6x+30}$a s v
  g) $\dfrac{6y^3-15y^2}{24y^2-60y}$a s v
  h) $\dfrac{24a^4-40a^3}{60a^6-100a^5}$a s v
  
  ## Question 12
  
  Simplify using any method
  
  a) $\dfrac{4x^2+6x+2}{10}$a s v
  b) $\dfrac{18p^4-15p}{33+15p^3}$a s v
  c) $\dfrac{15x^3+15x^2y}{5x^2+5xy}$a s v
  d) $\dfrac{x-2}{2-x}$a s v
  e) $\dfrac{5(x-9)}{9-x}$a s v
  f) $\dfrac{7x-35}{5-x}$a s v
  g) $\dfrac{3x^2-33x}{44-4x}$a s v
  h) $\dfrac{40y^2-100y}{20y^2-8y^3}$a s v
  
  ## Question 13
  
  Factorise and simplify
  
  a) $\dfrac{x^2+2x}{x^2+3x+2}$a s v
  b) $\dfrac{x^2+7x+10}{2x^2+10x}$a s v
  c) $\dfrac{x^2+4x+3}{x^2+9x+18}$a s v
  d) $\dfrac{x^2+14x+45}{x^2+9x+20}$a s v
  e) $\dfrac{x^2+13x+30}{x+10}$a s v
  f) $\dfrac{x^2+3x-18}{x^2+8x+12}$a s v
  g) $\dfrac{x^2-6x+8}{x^2-9x+14}$a s v
  h) $\dfrac{x^2-14x+49}{x^2-16x+63}$a s v
  
  ## Question 14
  
  Factorise and simplify
  
  a) $\dfrac{3x^2+9x}{2x^2+7x+3}$a s v
  b) $\dfrac{2x^2+19x+35}{10x^2+25x}$a s v
  c) $\dfrac{3x^2+7x+2}{3x^2+10x+3}$a s v
  d) $\dfrac{5x^2+32x+12}{5x^2-8x-4}$a s v
  e) $\dfrac{9x^2+16x+5}{6x^2+19x+15}$a s v
  f) $\dfrac{4x^2+28x+49}{10x^2+37x+7}$a s v
  g) $\dfrac{12x^2+29x-8}{9x^2+21x-8}$a s v
  h) $\dfrac{6x^2-43x+72}{8x^2-54x+81}$a s v
  
  ## Question 15
  
  Factorise and simplify
  
  a) $\dfrac{3x^2+24x+45}{x^3+11x^2+30x}$a s v
  b) $\dfrac{4x^3+60x^2+224x}{9x^2+54x-144}$a s v
  c) $\dfrac{y^4-10y^3+16y^2}{60y-4y^2-216}$a s v
  d) $\dfrac{42a^2-315a+525}{315a-36a^2-36a^3}$a s v
explanation: The document is a set of algebra exercises focused on simplifying algebraic fractions. Each question is presented with multiple parts (a, b, c, etc.), and each part is followed by placeholders for an answer (a), solution (s), and video (v). The document contains multiple questions, each with multiple parts, but no answers or solutions are provided in the text.
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distilabel_metadata.content: # Algebra - Simplifying Algebraic Fractions
  
  a - answer    s - solution    v - video
  
  ## Question 1
  
  Simplify
  
  a) $\dfrac{6x}{4}$a s v
  b) $\dfrac{8x}{6}$a s v
  c) $\dfrac{8x}{10}$a s v
  d) $\dfrac{21x^2}{14}$a s v
  e) $\dfrac{46y}{2}$a s v
  f) $\dfrac{9\sqrt{a}}{27}$a s v
  
  ## Question 2
  
  Simplify
  
  a) $\dfrac{15}{10x}$a s v
  b) $\dfrac{40}{30y}$a s v
  c) $\dfrac{16}{4p}$a s v
  d) $\dfrac{48}{20a^3}$a s v
  e) $\dfrac{9}{14h}$a s v
  f) $\dfrac{36}{32m}$a s v
  
  ## Question 3
  
  Simplify
  
  a) $\dfrac{2y}{3y}$a s v
  b) $\dfrac{10x}{4x}$a s v
  c) $\dfrac{15z}{5z}$a s v
  d) $\dfrac{5x^2}{5x^2}$a s v
  e) $\dfrac{2\sqrt{y}}{7\sqrt{y}}$a s v
  f) $\dfrac{48y^5}{36y^5}$a s v
  
  ## Question 4
  
  Simplify
  
  a) $\dfrac{3x^2}{2x}$a s v
  b) $\dfrac{9p^3}{5p}$a s v
  c) $\dfrac{5y^2}{y}$a s v
  d) $\dfrac{16z^5}{12z^2}$a s v
  e) $\dfrac{21q^8}{35q^3}$a s v
  f) $\dfrac{44c^{12}}{20c^{12}}$a s v
  
  ## Question 5
  
  Simplify
  
  a) $\dfrac{4x}{5x^3}$a s v
  b) $\dfrac{8x^2}{6x^5}$a s v
  c) $\dfrac{9v^3}{15v^3}$a s v
  d) $\dfrac{35y^4}{50y^{17}}$a s v
  e) $\dfrac{42a^4}{24a^5}$a s v
  f) $\dfrac{19t^{13}}{3t^{13}}$a s v
  
  ## Question 6
  
  Simplify
  
  a) $\dfrac{2(x+1)}{3(x+1)}$a s v
  b) $\dfrac{18(y-2)}{6(y-2)}$a s v
  c) $\dfrac{22(x^2+4)}{10(x+1)}$a s v
  d) $\dfrac{15(x-1)}{39(x-1)^2}$a s v
  e) $\dfrac{77(2x+3)^3}{44(2x+3)}$a s v
  f) $\dfrac{8(4z^2+5)^8}{11(4z^2+5)^{10}}$a s v
  
  ## Question 7
  
  Simplify
  
  a) $\dfrac{x^2y}{x}$a s v
  b) $\dfrac{4xy^7}{xy^2}$a s v
  c) $\dfrac{20x^4y^2}{15x^3}$a s v
  d) $\dfrac{10a^6}{25a^2b^5}$a s v
  e) $\dfrac{4x(x+5)}{3(x+5)}$a s v
  f) $\dfrac{48h^2(g-3)}{40h}$a s v
  
  ## Question 8
  
  Simplify. Leave answers with positive indices
  
  a) $\dfrac{5x}{x^{-2}y}$a s v
  b) $\dfrac{4y^{-3}}{xy}$a s v
  c) $\dfrac{2x^{-5}y^{-3}}{10x^{-1}y^{-2}}$a s v
  d) $\dfrac{15a^{-2}b^{-5}}{6a^{-6}bc^{-1}}$a s v
  e) $\dfrac{21x^{-3}y^4z}{56x^{-8}y^{-1}z^3}$a s v
  f) $\dfrac{108m^{-9}npq^{-15}}{60m^{-2}n^{-12}p^5}$a s v
  
  ## Question 9
  
  Simplify. Leave answers with positive indices
  
  a) $\dfrac{-4a^2bc}{2ab^2}$a s v
  b) $\dfrac{10xy^3}{-6xyz}$a s v
  c) $\dfrac{-8p^3q^2r}{-20pq^2r^3}$a s v
  d) $\dfrac{45p^{-2}q^4}{25p^7q^{-1}}$a s v
  e) $\dfrac{33c^{-1}d^{-7}e}{-21c^{-1}d^3e^8}$a s v
  f) $\dfrac{-27w^{-3}x^{14}y^{-9}z}{-63w^2x^{-3}z^{15}}$a s v
  
  ## Question 10
  
  Factorise and simplify
  
  a) $\dfrac{6x+4}{4}$a s v
  b) $\dfrac{8p-14}{2}$a s v
  c) $\dfrac{15w+35}{20}$a s v
  d) $\dfrac{21a-30}{12}$a s v
  e) $\dfrac{18a^2-20a}{14a}$a s v
  f) $\dfrac{42g^2-66g^5}{24g^3}$a s v
  
  ## Question 11
  
  Factorise and simplify
  
  a) $\dfrac{4x+8}{6x+12}$a s v
  b) $\dfrac{9x+3}{3x+1}$a s v
  c) $\dfrac{x^2+3x}{2x+6}$a s v
  d) $\dfrac{xy-2y}{4x-8}$a s v
  e) $\dfrac{8x+2y}{20x+5y}$a s v
  f) $\dfrac{4x^2+20x}{6x+30}$a s v
  g) $\dfrac{6y^3-15y^2}{24y^2-60y}$a s v
  h) $\dfrac{24a^4-40a^3}{60a^6-100a^5}$a s v
  
  ## Question 12
  
  Simplify using any method
  
  a) $\dfrac{4x^2+6x+2}{10}$a s v
  b) $\dfrac{18p^4-15p}{33+15p^3}$a s v
  c) $\dfrac{15x^3+15x^2y}{5x^2+5xy}$a s v
  d) $\dfrac{x-2}{2-x}$a s v
  e) $\dfrac{5(x-9)}{9-x}$a s v
  f) $\dfrac{7x-35}{5-x}$a s v
  g) $\dfrac{3x^2-33x}{44-4x}$a s v
  h) $\dfrac{40y^2-100y}{20y^2-8y^3}$a s v
  
  ## Question 13
  
  Factorise and simplify
  
  a) $\dfrac{x^2+2x}{x^2+3x+2}$a s v
  b) $\dfrac{x^2+7x+10}{2x^2+10x}$a s v
  c) $\dfrac{x^2+4x+3}{x^2+9x+18}$a s v
  d) $\dfrac{x^2+14x+45}{x^2+9x+20}$a s v
  e) $\dfrac{x^2+13x+30}{x+10}$a s v
  f) $\dfrac{x^2+3x-18}{x^2+8x+12}$a s v
  g) $\dfrac{x^2-6x+8}{x^2-9x+14}$a s v
  h) $\dfrac{x^2-14x+49}{x^2-16x+63}$a s v
  
  ## Question 14
  
  Factorise and simplify
  
  a) $\dfrac{3x^2+9x}{2x^2+7x+3}$a s v
  b) $\dfrac{2x^2+19x+35}{10x^2+25x}$a s v
  c) $\dfrac{3x^2+7x+2}{3x^2+10x+3}$a s v
  d) $\dfrac{5x^2+32x+12}{5x^2-8x-4}$a s v
  e) $\dfrac{9x^2+16x+5}{6x^2+19x+15}$a s v
  f) $\dfrac{4x^2+28x+49}{10x^2+37x+7}$a s v
  g) $\dfrac{12x^2+29x-8}{9x^2+21x-8}$a s v
  h) $\dfrac{6x^2-43x+72}{8x^2-54x+81}$a s v
  
  ## Question 15
  
  Factorise and simplify
  
  a) $\dfrac{3x^2+24x+45}{x^3+11x^2+30x}$a s v
  b) $\dfrac{4x^3+60x^2+224x}{9x^2+54x-144}$a s v
  c) $\dfrac{y^4-10y^3+16y^2}{60y-4y^2-216}$a s v
  d) $\dfrac{42a^2-315a+525}{315a-36a^2-36a^3}$a s v
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The document is a set of algebra exercises focused on simplifying algebraic fractions. Each question is presented with multiple parts (a, b, c, etc.), and each part is followed by placeholders for an answer (a), solution (s), and video (v). The document contains multiple questions, each with multiple parts, but no answers or solutions are provided in the text.
  
  Label: multiple-question