The expression $\frac{2x^2-x}{(x+1)(x-2)}-\frac{4+x}{(x+1)(x-2)}$ cannot be evaluated for $x=-1$ or $x=2$, 
since division by zero is not allowed. For other values of $x$: 
$\textbf{(A)}\ \text{The expression takes on many different values.}\\ \textbf{(B)}\ \text{The expression has only the value 2.}\\ \textbf{(C)}\ \text{The expression has only the value 1.}\\ \textbf{(D)}\ \text{The expression always has a value between }-1\text{ and }+2.\\ \textbf{(E)}\ \text{The expression has a value greater than 2 or less than }-1.$
$\frac{2x^2-x}{(x+1)(x-2)}-\frac{4+x}{(x+1)(x-2)} = \frac{2x^2-2x-4}{(x+1)(x-2)}$
This can be factored as $\frac{(2)(x^2-x-2)}{(x+1)(x-2)} \implies \frac{(2)(x+1)(x-2)}{(x+1)(x-2)}$, which cancels out to $2 \implies \boxed{\textbf{(B)} \text{The expression has only the value 2}}$.



[1954 AHSC](https://artofproblemsolving.com/wiki/index.php/1954_AHSME) ([Problems](https://artofproblemsolving.com/wiki/index.php/1954_AHSME_Problems) • [Answer Key](https://artofproblemsolving.com/wiki/index.php/1954_AHSME_Answer_Key) • [Resources](https://artofproblemsolving.comhttp://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=44&year=1954))


Preceded by[Problem 21](https://artofproblemsolving.com/wiki/index.php/1954_AHSME_Problems/Problem_21)

Followed by[Problem 23](https://artofproblemsolving.com/wiki/index.php/1954_AHSME_Problems/Problem_23)


[1](https://artofproblemsolving.com/wiki/index.php/1954_AHSME_Problems/Problem_1) • [2](https://artofproblemsolving.com/wiki/index.php/1954_AHSME_Problems/Problem_2) • [3](https://artofproblemsolving.com/wiki/index.php/1954_AHSME_Problems/Problem_3) • [4](https://artofproblemsolving.com/wiki/index.php/1954_AHSME_Problems/Problem_4) • [5](https://artofproblemsolving.com/wiki/index.php/1954_AHSME_Problems/Problem_5) • [6](https://artofproblemsolving.com/wiki/index.php/1954_AHSME_Problems/Problem_6) • [7](https://artofproblemsolving.com/wiki/index.php/1954_AHSME_Problems/Problem_7) • [8](https://artofproblemsolving.com/wiki/index.php/1954_AHSME_Problems/Problem_8) • [9](https://artofproblemsolving.com/wiki/index.php/1954_AHSME_Problems/Problem_9) • [10](https://artofproblemsolving.com/wiki/index.php/1954_AHSME_Problems/Problem_10) • [11](https://artofproblemsolving.com/wiki/index.php/1954_AHSME_Problems/Problem_11) • [12](https://artofproblemsolving.com/wiki/index.php/1954_AHSME_Problems/Problem_12) • [13](https://artofproblemsolving.com/wiki/index.php/1954_AHSME_Problems/Problem_13) • [14](https://artofproblemsolving.com/wiki/index.php/1954_AHSME_Problems/Problem_14) • [15](https://artofproblemsolving.com/wiki/index.php/1954_AHSME_Problems/Problem_15) • [16](https://artofproblemsolving.com/wiki/index.php/1954_AHSME_Problems/Problem_16) • [17](https://artofproblemsolving.com/wiki/index.php/1954_AHSME_Problems/Problem_17) • [18](https://artofproblemsolving.com/wiki/index.php/1954_AHSME_Problems/Problem_18) • [19](https://artofproblemsolving.com/wiki/index.php/1954_AHSME_Problems/Problem_19) • [20](https://artofproblemsolving.com/wiki/index.php/1954_AHSME_Problems/Problem_20) • [21](https://artofproblemsolving.com/wiki/index.php/1954_AHSME_Problems/Problem_21) • 22 • [23](https://artofproblemsolving.com/wiki/index.php/1954_AHSME_Problems/Problem_23) • [24](https://artofproblemsolving.com/wiki/index.php/1954_AHSME_Problems/Problem_24) • [25](https://artofproblemsolving.com/wiki/index.php/1954_AHSME_Problems/Problem_25) • [26](https://artofproblemsolving.com/wiki/index.php/1954_AHSME_Problems/Problem_26) • [27](https://artofproblemsolving.com/wiki/index.php/1954_AHSME_Problems/Problem_27) • [28](https://artofproblemsolving.com/wiki/index.php/1954_AHSME_Problems/Problem_28) • [29](https://artofproblemsolving.com/wiki/index.php/1954_AHSME_Problems/Problem_29) • [30](https://artofproblemsolving.com/wiki/index.php/1954_AHSME_Problems/Problem_30) • [31](https://artofproblemsolving.com/wiki/index.php/1954_AHSME_Problems/Problem_31) • [32](https://artofproblemsolving.com/wiki/index.php/1954_AHSME_Problems/Problem_32) • [33](https://artofproblemsolving.com/wiki/index.php/1954_AHSME_Problems/Problem_33) • [34](https://artofproblemsolving.com/wiki/index.php/1954_AHSME_Problems/Problem_34) • [35](https://artofproblemsolving.com/wiki/index.php/1954_AHSME_Problems/Problem_35) • [36](https://artofproblemsolving.com/wiki/index.php/1954_AHSME_Problems/Problem_36) • [37](https://artofproblemsolving.com/wiki/index.php/1954_AHSME_Problems/Problem_37) • [38](https://artofproblemsolving.com/wiki/index.php/1954_AHSME_Problems/Problem_38) • [39](https://artofproblemsolving.com/wiki/index.php/1954_AHSME_Problems/Problem_39) • [40](https://artofproblemsolving.com/wiki/index.php/1954_AHSME_Problems/Problem_40) • [41](https://artofproblemsolving.com/wiki/index.php/1954_AHSME_Problems/Problem_41) • [42](https://artofproblemsolving.com/wiki/index.php/1954_AHSME_Problems/Problem_42) • [43](https://artofproblemsolving.com/wiki/index.php/1954_AHSME_Problems/Problem_43) • [44](https://artofproblemsolving.com/wiki/index.php/1954_AHSME_Problems/Problem_44) • [45](https://artofproblemsolving.com/wiki/index.php/1954_AHSME_Problems/Problem_45) • [46](https://artofproblemsolving.com/wiki/index.php/1954_AHSME_Problems/Problem_46) • [47](https://artofproblemsolving.com/wiki/index.php/1954_AHSME_Problems/Problem_47) • [48](https://artofproblemsolving.com/wiki/index.php/1954_AHSME_Problems/Problem_48) • [49](https://artofproblemsolving.com/wiki/index.php/1954_AHSME_Problems/Problem_49) • [50](https://artofproblemsolving.com/wiki/index.php/1954_AHSME_Problems/Problem_50)


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