Question

simplify x^2+2x/12x+54-3-x/8x+36

Answer 1

factor, then combine fractions
\[\frac{x^{2}+2x}{12x+54}-\frac{3-x}{8x+36}\]
\[=\frac{x(x+2)}{6(2x+9)}-\frac{3-x}{4(2x+9)}\]
\[=\frac{2x(x+2)}{12(2x+9)} - \frac{3(3-x)}{12(2x+9)}\]
\[=\frac{2x(x+2) -3(3-x)}{12(2x+9)}\]
\[=\frac{2x^{2}+7x-9}{12(2x+9)}\]
\[=\frac{(x-1)(2x+9)}{12(2x+9)}\]
\[=\frac{x-1}{12}\]