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

The solution to (x+3)/(6x^2+x-2)-1/(4x^2-4x+1) is (2x^2+2x-5)/((2x-1)^2(3x+2))

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

simplify

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

\frac{2 x ^{2} + 2 x - 5}{( 2 x - 1 ) ^{2} ( 3 x + 2 )}

Solution steps

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

Least Common Multiplier of

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

Adjust Fractions based on the LCM

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

Apply the fraction rule:

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

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

Simplify

(x + 3) (2 x - 1) - (3 x + 2) : 2 x^{2} + 2 x - 5

= \frac{2 x ^{2} + 2 x - 5}{( 2 x - 1 ) ^{2} ( 3 x + 2 )}

(x y^{2})^{3}

8 1^{0.5 l o g_{9} (7)} + lo g_{81} (3)

3 i (2 i^{2} - 5 i)

\frac{x ^{2} - 11 x + 28}{x ^{3} - 4 x ^{2}}

(- 1)^{35}

What is (x+3)/(6x^2+x-2)-1/(4x^2-4x+1) ?
The solution to (x+3)/(6x^2+x-2)-1/(4x^2-4x+1) is (2x^2+2x-5)/((2x-1)^2(3x+2))