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.12² - 27/6x² +33x + 36Rational expression in lowest terms:Variable restrictions for the original expression: x

Answer 1

Step-by-step explanation:

The expression is given below as

`(12x^2-27)/(6x^2+33x+36)`

Step 1:

Simplify both the numerator and denominator

`\begin{gathered} (12x^(2)-27)/(6x^(2)+33x+36) \\ 12x^2-27=3(4x^2-9)=3(2x-3)(2x+3) \\ 6x^2+33x+36=3(2x^2+11x+12) \\ 3(2x^2+11x+12)=3(2x^2+8x+3x+12) \\ 3(2x^2+11x+12)=3(2x(x+4)+3(x+4) \\ 3(2x^2+11x+12)=3(2x+3)(x+4) \end{gathered}`

By rewritng the expression , we will have

`\begin{gathered} (12x^(2)-27)/(6x^(2)+33x+36)=(3(2x+3)(2x-3))/(3(x+4)(2x+3)) \\ (12x^(2)-27)/(6x^(2)+33x+36)=(2x-3)/(x+4) \end{gathered}`

Hence,

The simplified expression will be

`(2x-3)/(x+4)`

The variable restriction of the original expression will be

`\begin{gathered} 3(2x+3)(x+4)=0 \\ 2x+3=0,x+4=0 \\ 2x=-3,x=-4 \\ x=-(3)/(2),x=-4 \end{gathered}`

Hence,

The variable restriction for the original expression will be

`x\\e-(3)/(2),-4`