How do you solve #5- \frac { a - 11} { a + 4} = \frac { a ^ { 2} - 1} { a + 4}#?

1 Answer
Dec 28, 2016

#a = 8#

Explanation:

#5 - (a-11)/(a+4) = (a^2-1)/(a+4)#

#5 = (a^2-1)/(a+4) + (a-11)/(a+4)#

#5 = ((a^2-1)+(a-11))/(a+4)#

#5(a+4) = a^2-1+a-11#

#5a+20 = a^2+a-12#

#0 = a^2+a-12-5a-20#

#0 = a^2-4a-32#

#0=(a-8)(a+4)#

#a-8 = 0, a+4 = 0#

#a = 8, a = -4#

#a!=-4#, because it would result in dividing by #0#

#a=8#