Question

Multiply the rational expressions and express the product in simplest form. When typing your answer for the numerator and denominator be sure to type the term with the variable first.\frac{\left(2x^2+9x-35\right)}{\left(x^2+10x+21\right)}\cdot \frac{\left(3x^2+2x-21\right)}{\left(3x^2+14x-49\right)}The numerator is AnswerThe denominator is Answer

Answer 1

Given:

The expression is,

$\frac{(2x^2+9x-35)}{(x^2+10x+21)}\times\frac{(3x^2+2x-21)}{(3x^2+14x-49)}$

Simplify the expression,

$\begin{gathered} \frac{(2x^2+9x-35)}{(x^2+10x+21)}\times\frac{(3x^2+2x-21)}{(3x^2+14x-49)} \\ =\frac{2x^2-5x+14x-35}{x^2+3x+7x+21}\times\frac{3x^2-7x+9x-21}{3x^2-7x+21x-49} \\ =\frac{x(2x^{}-5)+7(2x-5)}{x(x^{}+3)+7(x+3)}\times\frac{x(3x^{}-7)+3(3x-7)}{x(3x^{}-7)+7(3x-7)} \\ =\frac{(2x-5)(x+7)}{(x+3)(x+7)}\times\frac{(3x-7)(x+3)}{(3x-7)(x+7)} \\ \text{Cancel the common factor } \\ =\frac{2x-5}{x+3}\times\frac{x+3}{x+7} \\ =\frac{2x-5}{x+7} \end{gathered}$

Answer:

Numerator is 2x - 5.

Denominator is x + 7.