What is (a^2-4a+4)/(a^2+ab-2a-2b) ?

The solution to (a^2-4a+4)/(a^2+ab-2a-2b) is (a-2)/(a+b)

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simplify (a^2-4a+4)/(a^2+ab-2a-2b)

simplify

\frac{a ^{2} - 4 a + 4}{a ^{2} + ab - 2 a - 2 b}

\frac{a - 2}{a + b}

Solution steps

\frac{a ^{2} - 4 a + 4}{a ^{2} + ab - 2 a - 2 b}

Factor

a^{2} - 4 a + 4 : (a - 2)^{2}

= \frac{( a - 2 ) ^{2}}{a ^{2} + ab - 2 a - 2 b}

Factor

a^{2} + ab - 2 a - 2 b : (a + b) (a - 2)

= \frac{( a - 2 ) ^{2}}{( a + b ) ( a - 2 )}

Apply exponent rule:

a^{b + c} = a^{b} \cdot a^{c}

(a - 2)^{2} = (a - 2) (a - 2)

= \frac{( a - 2 ) ( a - 2 )}{( a + b ) ( a - 2 )}

Cancel the common factor:

a - 2

= \frac{a - 2}{a + b}

\frac{75}{12}

(7 a - 5 b)^{2}

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

2 sin (x) \cdot cos (x)

What is (a^2-4a+4)/(a^2+ab-2a-2b) ?
The solution to (a^2-4a+4)/(a^2+ab-2a-2b) is (a-2)/(a+b)