What is 3/(5x+2)+(5x)/(25x^2-4) ?

The solution to 3/(5x+2)+(5x)/(25x^2-4) is (20x-6)/((5x+2)(5x-2))

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simplify 3/(5x+2)+(5x)/(25x^2-4)

simplify

\frac{3}{5 x + 2} + \frac{5 x}{25 x ^{2} - 4}

\frac{20 x - 6}{( 5 x + 2 ) ( 5 x - 2 )}

Solution steps

\frac{3}{5 x + 2} + \frac{5 x}{25 x ^{2} - 4}

Least Common Multiplier of

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

Adjust Fractions based on the LCM

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

Apply the fraction rule:

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

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

Simplify

3 (5 x - 2) + 5 x : 20 x - 6

= \frac{20 x - 6}{( 5 x + 2 ) ( 5 x - 2 )}

- \frac{4}{3} \times (- 3)

\frac{5}{9} - \frac{1}{9}

2 π \times 3

\frac{1}{12} + \frac{11}{8}

5 x - 1 x - 12

What is 3/(5x+2)+(5x)/(25x^2-4) ?
The solution to 3/(5x+2)+(5x)/(25x^2-4) is (20x-6)/((5x+2)(5x-2))