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

2 Answers
Kenneth B
Feb 28, 2017

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

Explanation:

  1. #-(4a) / (a+8) = 12 / (a-13)# (Rewrite the equation)
  2. #12(-a-8) = -4a(a-13)# (Cross multiply)
  3. #-12a-96 = -4a^2+52a# (Simplify)
  4. #4a^2-64a-96=0# (Set the equation equal to 0)
  5. #4(a^2-16-24)=0# (Factor out the 4)
  6. #a=16+-sqrt(256+96)/2# (Simplify using the quadratic formula)
  7. #a=6+-(4sqrt(22))/2# (Simplify)
  8. #a=6+-2sqrt(22)# (Final answer)
EZ as pi
Feb 28, 2017

#a =6 " or " a=4#

Explanation:

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#

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