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,

`(14x^2-45x-14)/(21x^2-50x-16)`

Simplify

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

Hence, Rational expression in lowest terms is,

`(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=-(2)/(7),x=(8)/(3) \\ \therefore x\\e(2)/(7),(8)/(3) \end{gathered}`

Hence, the answer is

`\begin{equation*} x\\e(2)/(7),(8)/(3) \end{equation*}`