vereinfachen (2.5w^2+2w-0.5)/((w-1)^2)-1

Lösung

vereinfachen

\frac{2.5 w ^{2} + 2 w - 0.5}{( w - 1 ) ^{2}} - 1

\frac{1.5 w ^{2} + 4 w - 1.5}{( w - 1 ) ^{2}}

Schritte zur Lösung

\frac{2.5 w ^{2} + 2 w - 0.5}{( w - 1 ) ^{2}} - 1

Wende Bruchregel an:

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

= \frac{- 1 \cdot ( w - 1 ) ^{2} + 2.5 w ^{2} + 2 w - 0.5}{( w - 1 ) ^{2}}

Apply rule:

1 \cdot a = a

- 1 \cdot (w - 1)^{2} = - (w - 1)^{2}

= \frac{- ( w - 1 ) ^{2} + 2.5 w ^{2} + 2 w - 0.5}{( w - 1 ) ^{2}}

Vereinfache

- (w - 1)^{2} + 2.5 w^{2} + 2 w - 0.5 : 1.5 w^{2} + 4 w - 1.5

= \frac{1.5 w ^{2} + 4 w - 1.5}{( w - 1 ) ^{2}}

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e x p an d (x cos (a) - y sin (a))^{2}