What is (4m)/(4m^2-1)-(2m+1)/(6m-3)+(2m-1)/(4m+2) ?

The solution to (4m)/(4m^2-1)-(2m+1)/(6m-3)+(2m-1)/(4m+2) is (2m+1)/(6(2m-1))

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simplify (4m)/(4m^2-1)-(2m+1)/(6m-3)+(2m-1)/(4m+2)

simplify

\frac{4 m}{4 m ^{2} - 1} - \frac{2 m + 1}{6 m - 3} + \frac{2 m - 1}{4 m + 2}

\frac{2 m + 1}{6 ( 2 m - 1 )}

Solution steps

\frac{4 m}{4 m ^{2} - 1} - \frac{2 m + 1}{6 m - 3} + \frac{2 m - 1}{4 m + 2}

Least Common Multiplier of

4 m^{2} - 1, 6 m - 3, 4 m + 2 : 6 (2 m + 1) (2 m - 1)

Adjust Fractions based on the LCM

= \frac{24 m}{6 ( 2 m + 1 ) ( 2 m - 1 )} - \frac{2 ( 2 m + 1 ) ^{2}}{6 ( 2 m + 1 ) ( 2 m - 1 )} + \frac{3 ( 2 m - 1 ) ^{2}}{6 ( 2 m + 1 ) ( 2 m - 1 )}

Apply the fraction rule:

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

= \frac{24 m - 2 ( 2 m + 1 ) ^{2} + 3 ( 2 m - 1 ) ^{2}}{6 ( 2 m + 1 ) ( 2 m - 1 )}

Simplify

24 m - 2 (2 m + 1)^{2} + 3 (2 m - 1)^{2} : 4 m^{2} + 4 m + 1

= \frac{4 m ^{2} + 4 m + 1}{6 ( 2 m + 1 ) ( 2 m - 1 )}

Cancel

\frac{4 m ^{2} + 4 m + 1}{6 ( 2 m + 1 ) ( 2 m - 1 )} : \frac{2 m + 1}{6 ( 2 m - 1 )}

= \frac{2 m + 1}{6 ( 2 m - 1 )}

(\frac{12}{7})^{2}

\frac{5}{18} - \frac{16}{63} + \frac{1}{12}

∣ 9 x ∣ = 8

2 x - x^{2} = 0

2 v^{2} + 5 v + 2

What is (4m)/(4m^2-1)-(2m+1)/(6m-3)+(2m-1)/(4m+2) ?
The solution to (4m)/(4m^2-1)-(2m+1)/(6m-3)+(2m-1)/(4m+2) is (2m+1)/(6(2m-1))