Question

What is the simplified form of this rational expression? 6x^2-54/5x^2+15x

Answer 1

Answer:

The simplified form of the expression is $\frac{6x^2-54}{5x^2+15x}=\frac{6(x-3)}{5x}$            

Step-by-step explanation:

Given : Expression  $\frac{6x^2-54}{5x^2+15x}$

To find : What is the simplified form of this rational expression?

Solution :

Step 1 - Write the expression

$=\frac{6x^2-54}{5x^2+15x}$

Step 2 - Factor the numerator and denominator,

$=\frac{6(x^2-9)}{5x(x+3)}$

$=\frac{6(x-3)(x+3)}{5x(x+3)}$

Step 3 - Cancel the factor (x+3) from numerator and denominator,

$=\frac{6(x-3)}{5x}$

Therefore, The simplified form of the expression is $\frac{6x^2-54}{5x^2+15x}=\frac{6(x-3)}{5x}$

Answer 2

Factor the numerator and denominator then simplify.

6x^2 - 54          6(x^2 - 9)          6(x + 3)(x - 3)        6(x - 3)
--------------  =    -------------     =  ------------------  =  ------------
5x^2 + 15x      5x(x + 3)            5x(x + 3)                5x


6(x - 3)
----------
5x