How do you evaluate $\frac{a - b}{4 a + 4 b} + \div \frac{a^{2} - b^{2}}{a^{2} + 8 a + 16}$ $frac { a - b } { 4a + 4b } +\div \frac { a ^ { 2} - b ^ { 2} } { a ^ { 2} + 8a + 16}$ ?

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Answer 1 · 2017-12-03T22:50:23

$\frac{a^{2} + 8 a + 16}{4 a^{2} + 8 a b + 4 b^{2}}$ $(a^2+8a+16)/(4a^2+8ab+4b^2)$

Definitely going to want to start by factoring this.

$\frac{a - b}{4 (a + b)} \div \frac{(a - b) (a + b)}{{(a + 4)}^{2}}$ $(a-b)/(4(a+b))divide((a-b)(a+b))/(a+4)^2$

"Keep-change-flip" so we have multiplication:

$\frac{a - b}{4 (a + b)} \times \frac{{(a + 4)}^{2}}{(a - b) (a + b)}$ $(a-b)/(4(a+b))times(a+4)^2/((a-b)(a+b))$

$color(red)cancel(color(black)(a-b))/(4(a+b))times(a+4)^2/(color(red)cancel(color(black)(a-b))(a+b))$

$(a+4)^2/(4(a+b)^2)$

If you wish, multiply out:

$(a^2+8a+16)/(4a^2+8ab+4b^2)$

How do you evaluate frac { a - b } { 4a + 4b } +\div \frac { a ^ { 2} - b ^ { 2} } { a ^ { 2} + 8a + 16}a−b4a+4b+÷a2−b2a2+8a+16frac { a - b } { 4a + 4b } +\div \frac { a ^ { 2} - b ^ { 2} } { a ^ { 2} + 8a + 16}?