What is x/(2x-5)-(4x+15)/(4x^2-25) ?

The solution to x/(2x-5)-(4x+15)/(4x^2-25) is (x+3)/(2x+5)

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simplify x/(2x-5)-(4x+15)/(4x^2-25)

simplify

\frac{x}{2 x - 5} - \frac{4 x + 15}{4 x ^{2} - 25}

\frac{x + 3}{2 x + 5}

Solution steps

\frac{x}{2 x - 5} - \frac{4 x + 15}{4 x ^{2} - 25}

Least Common Multiplier of

2 x - 5, 4 x^{2} - 25 : (2 x - 5) (2 x + 5)

Adjust Fractions based on the LCM

= \frac{x ( 2 x + 5 )}{( 2 x - 5 ) ( 2 x + 5 )} - \frac{4 x + 15}{( 2 x - 5 ) ( 2 x + 5 )}

Apply the fraction rule:

\frac{a}{c} - \frac{b}{c} = \frac{a - b}{c}

= \frac{x ( 2 x + 5 ) - ( 4 x + 15 )}{( 2 x - 5 ) ( 2 x + 5 )}

Simplify

x (2 x + 5) - (4 x + 15) : 2 x^{2} + x - 15

= \frac{2 x ^{2} + x - 15}{( 2 x - 5 ) ( 2 x + 5 )}

Cancel

\frac{2 x ^{2} + x - 15}{( 2 x - 5 ) ( 2 x + 5 )} : \frac{x + 3}{2 x + 5}

= \frac{x + 3}{2 x + 5}

2 \times 8

- (5 n + 5.8 p) - 7

5 \times 24

x^{3} \times 1

5 - \frac{3 ^{2}}{2}

What is x/(2x-5)-(4x+15)/(4x^2-25) ?
The solution to x/(2x-5)-(4x+15)/(4x^2-25) is (x+3)/(2x+5)