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

The solution to (y^2-1)/(y+1)-3/(y-1) is (y^2-2y-2)/(y-1)

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

simplify

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

\frac{y ^{2} - 2 y - 2}{y - 1}

Solution steps

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

Least Common Multiplier of

y + 1, y - 1 : (y + 1) (y - 1)

Adjust Fractions based on the LCM

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

Apply the fraction rule:

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

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

Simplify

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

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

Cancel

\frac{y ^{3} - y ^{2} - 4 y - 2}{( y + 1 ) ( y - 1 )} : \frac{y ^{2} - 2 y - 2}{y - 1}

= \frac{y ^{2} - 2 y - 2}{y - 1}

lo g_{7} (343)

(2)^{2} + (23)^{2}

\frac{\frac{1}{3}}{\frac{1}{6}}

(9 - 5 i)^{2}

(1 + 2 x)^{6}

What is (y^2-1)/(y+1)-3/(y-1) ?
The solution to (y^2-1)/(y+1)-3/(y-1) is (y^2-2y-2)/(y-1)