Answer:
The simplified form of the expression is [tex]\frac{6x^2-54}{5x^2+15x}=\frac{6(x-3)}{5x}[/tex]
Step-by-step explanation:
Given : Expression [tex]\frac{6x^2-54}{5x^2+15x}[/tex]
To find : What is the simplified form of this rational expression?
Solution :
Step 1 - Write the expression
[tex]=\frac{6x^2-54}{5x^2+15x}[/tex]
Step 2 - Factor the numerator and denominator,
[tex]=\frac{6(x^2-9)}{5x(x+3)}[/tex]
[tex]=\frac{6(x-3)(x+3)}{5x(x+3)}[/tex]
Step 3 - Cancel the factor (x+3) from numerator and denominator,
[tex]=\frac{6(x-3)}{5x}[/tex]
Therefore, The simplified form of the expression is [tex]\frac{6x^2-54}{5x^2+15x}=\frac{6(x-3)}{5x}[/tex]
