What is 2/(x-5)+(3x)/(x^2-25) ?

The solution to 2/(x-5)+(3x)/(x^2-25) is (5x+10)/((x-5)(x+5))

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simplify 2/(x-5)+(3x)/(x^2-25)

simplify

\frac{2}{x - 5} + \frac{3 x}{x ^{2} - 25}

\frac{5 x + 10}{( x - 5 ) ( x + 5 )}

Solution steps

\frac{2}{x - 5} + \frac{3 x}{x ^{2} - 25}

Least Common Multiplier of

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

Adjust Fractions based on the LCM

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

Apply the fraction rule:

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

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

Simplify

2 (x + 5) + 3 x : 5 x + 10

= \frac{5 x + 10}{( x - 5 ) ( x + 5 )}

(x - 10) (x - 10)

(3 - 2 i) (4 + 3 i)

(- 7 x^{2} + 3) - (- 4 x - 3)

12 \times 6

1 3^{2} - 5^{2}

What is 2/(x-5)+(3x)/(x^2-25) ?
The solution to 2/(x-5)+(3x)/(x^2-25) is (5x+10)/((x-5)(x+5))