Question

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

Answer 1

The simplified form of the expression is
`(6x^2-54)/(5x^2+15x)=(6(x-3))/(5x)`

Explanation:

Given : Expression
`(6x^2-54)/(5x^2+15x)`

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

Solution :

Step 1 - Write the expression

`=(6x^2-54)/(5x^2+15x)`

Step 2 - Factor the numerator and denominator,

`=(6(x^2-9))/(5x(x+3))`

`=(6(x-3)(x+3))/(5x(x+3))`

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

`=(6(x-3))/(5x)`

Therefore, The simplified form of the expression is
`(6x^2-54)/(5x^2+15x)=(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