What is 3/a+2/(5a-3)+(1-85a)/(25a^2-9) ?

The solution to 3/a+2/(5a-3)+(1-85a)/(25a^2-9) is (7a-27)/(a(5a-3)(5a+3))

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simplify 3/a+2/(5a-3)+(1-85a)/(25a^2-9)

simplify

\frac{3}{a} + \frac{2}{5 a - 3} + \frac{1 - 85 a}{25 a ^{2} - 9}

\frac{7 a - 27}{a ( 5 a - 3 ) ( 5 a + 3 )}

Solution steps

\frac{3}{a} + \frac{2}{5 a - 3} + \frac{1 - 85 a}{25 a ^{2} - 9}

Least Common Multiplier of

a, 5 a - 3, 25 a^{2} - 9 : a (5 a - 3) (5 a + 3)

Adjust Fractions based on the LCM

= \frac{3 ( 5 a - 3 ) ( 5 a + 3 )}{a ( 5 a - 3 ) ( 5 a + 3 )} + \frac{2 a ( 5 a + 3 )}{a ( 5 a - 3 ) ( 5 a + 3 )} + \frac{( 1 - 85 a ) a}{a ( 5 a - 3 ) ( 5 a + 3 )}

Apply the fraction rule:

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

= \frac{3 ( 5 a - 3 ) ( 5 a + 3 ) + 2 a ( 5 a + 3 ) + ( 1 - 85 a ) a}{a ( 5 a - 3 ) ( 5 a + 3 )}

Simplify

3 (5 a - 3) (5 a + 3) + 2 a (5 a + 3) + (1 - 85 a) a : 7 a - 27

= \frac{7 a - 27}{a ( 5 a - 3 ) ( 5 a + 3 )}

\frac{24}{27}

8 + (- 6)

- 2!

- 1 i

\frac{85}{2}

What is 3/a+2/(5a-3)+(1-85a)/(25a^2-9) ?
The solution to 3/a+2/(5a-3)+(1-85a)/(25a^2-9) is (7a-27)/(a(5a-3)(5a+3))