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

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

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

simplify

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

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

Solution steps

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

Least Common Multiplier of

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

Adjust Fractions based on the LCM

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

Apply the fraction rule:

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

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

Simplify

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

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

\frac{21}{6}

(x - 1) (x + 2) (x - 3)

\frac{1}{7}

\frac{7 x}{x - 7} + \frac{7 x + 3}{x - 6}

\frac{5}{50}

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