For what value of $x$ will $\frac{3+x}{5+x}$ and $\frac{1+x}{2+x}$ be equal?
To solve for $x$, I need to set the two fractions equal to each other and cross-multiply. That is, I need to find $x$ such that $(3+x)(2+x) = (1+x)(5+x)$. I can expand the brackets on both sides and simplify the equation. On the left side, I get $6+5x+x^2$, and on the right side, I get $5+6x+x^2$. Subtracting $x^2$ from both sides, I get $6+5x = 5+6x$. Subtracting $5x$ from both sides, I get $6 = 5+x$. Subtracting $5$ from both sides, I get $x = 1$. So $x = 1$ is the correct value that makes the fractions equal. 