How do you solve $-\frac { 4a } { a + 8} = \frac { 12} { a - 13}$ ?

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Answer 1 · 2017-02-28T06:28:46

Cross multiply the fractions to get the answer.
$a=6+-2sqrt(22)$

Answer 2 · 2017-02-28T06:32:31

$a =6 " or " a=4$

Whenever you have an equation which has ONE term on each side and the term is a fraction, you can get rid of the fractions by cross-multiplying.

$color(blue)(-4a)/color(red)((a+8)) = color(red)(12)/color(blue)((a-13))$

$color(red)(12)xx color(red)((a+8))=color(blue)(-4a) xxcolor(blue)((a-13))" "larr$ multiply out the brackets

$12a+96 = -4a^2+52a" "larr$ a quadratic, so make it =0

$4a^2-52a+12a+96 =0$

$4a^2 -40a +96 =0" "larrdiv4$

$a^2 -10a+24 =0" "larr$ find factors

$(a-6)(a-4)=0$

$a =6 " or " a=4$

How do you solve -\frac { 4a } { a + 8} = \frac { 12} { a - 13}-\frac { 4a } { a + 8} = \frac { 12} { a - 13}?