Question

Reduce the rational expression to lowest terms. If it is already in lowest terms, enter the expression in the answer box. Also, specify any restrictions on the variable.14x²45x - 14/21x²50x16Rational expression in lowest terms:Variable restrictions for the original expression:

Answer 1

The expression given is,

$\frac{14x^2-45x-14}{21x^2-50x-16}$

Simplify

$\begin{gathered} =\frac{\left(7x+2\right)\left(2x-7\right)}{21x^2-50x-16} \\ =\frac{\left(7x+2\right)\left(2x-7\right)}{\left(7x+2\right)\left(3x-8\right)} \\ \mathrm{Cancel\:the\:common\:factor:}\:7x+2 \\ =\frac{2x-7}{3x-8} \end{gathered}$

Hence, Rational expression in lowest terms is,

$\frac{2x-7}{3x-8}$

Variable restrictions for the original expression:

$\begin{gathered} \left(7x+2\right)\left(3x-8\right)=0 \\ 7x+2=0,3x-8=0 \\ 7x=-2,3x=8 \\ x=-\frac{2}{7},x=\frac{8}{3} \\ \therefore x\ne\frac{2}{7},\frac{8}{3} \end{gathered}$

Hence, the answer is

$\begin{equation*} x\ne\frac{2}{7},\frac{8}{3} \end{equation*}$