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

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

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

simplify

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

\frac{3 x}{2 x - 1}

Solution steps

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

Factor

6 x^{2} + 3 x : 3 x (2 x + 1)

= \frac{3 x ( 2 x + 1 )}{4 x ^{2} - 1}

Factor

4 x^{2} - 1 : (2 x + 1) (2 x - 1)

= \frac{3 x ( 2 x + 1 )}{( 2 x + 1 ) ( 2 x - 1 )}

Cancel the common factor:

2 x + 1

= \frac{3 x}{2 x - 1}

15 - 3 x

7 - 7 (2 + 3 x) + 7

- 2 (2 x)^{2} + (2 x) - 1

6 y^{2} (2 y^{4})^{2}

\frac{1}{4} \div 6