How do you solve #\frac { 5} { x ^ { 2} + 6x - 7} - \frac { 3} { x - 1} = \frac { 9} { 3x + 21} #?

1 Answer
Mar 10, 2018

#x=(-13)/6#

Explanation:

Here,#x^2+6x-7=x^2+7x-x-7=x(x+7)-1(x+7)=(x+7)(x-1)#
Now.
#5/(x^2+6x-7)-3/(x-1)=9/(3x+21)#
#=>5/((x+7)(x-1))-3/(x-1)=cancel9^3/(cancel3(x+7))#
#=>5/((x+7)(x-1))-(3(x+7))/((x+7)(x-1))=(3(x-1))/((x+7)(x-1))#
#=>5-3(x+7)=3(x-1)#
#=>5-3x-21=3x-3#
#=>5-21+3=3x+3x=>6x=-13=>x=(-13)/6#