What is (6x^2+15x)/(12x^2-75) ?

The solution to (6x^2+15x)/(12x^2-75) is x/(2x-5)

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simplify (6x^2+15x)/(12x^2-75)

simplify

\frac{6 x ^{2} + 15 x}{12 x ^{2} - 75}

\frac{x}{2 x - 5}

Solution steps

\frac{6 x ^{2} + 15 x}{12 x ^{2} - 75}

Factor

6 x^{2} + 15 x : 3 x (2 x + 5)

= \frac{3 x ( 2 x + 5 )}{12 x ^{2} - 75}

Factor

12 x^{2} - 75 : 3 (2 x + 5) (2 x - 5)

= \frac{3 x ( 2 x + 5 )}{3 ( 2 x + 5 ) ( 2 x - 5 )}

Cancel the common factor:

3

= \frac{x ( 2 x + 5 )}{( 2 x + 5 ) ( 2 x - 5 )}

Cancel the common factor:

2 x + 5

= \frac{x}{2 x - 5}

\frac{x}{x + 3} + \frac{3}{x + 3} + \frac{2}{x + 3}

\frac{5}{3} + \frac{1}{3}

\frac{( 2 x ^{3} ) ( 8 x ^{5} )}{4 x ^{6}}

csc (x) tan (x)

What is (6x^2+15x)/(12x^2-75) ?
The solution to (6x^2+15x)/(12x^2-75) is x/(2x-5)