How do you solve for x: #12/(x+1) - 10/(x-3)=-3#?

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Answer 1 · 2016-06-25T08:33:41

#x = 5 or x= -11/3#

In an equation, we can get rid of the denominators by multiplying every term by the LCM of the denominators.

The LCM is this case is #color(red)((x+1)(x-3))#

#(12xxcolor(red)(cancel((x+1))(x-3)))/cancel((x+1)) -(10xx color(red)((x+1)cancel((x-3))))/cancel((x-3))= -3color(red)((x+1)(x-3))#

#12(x-3) - 10(x+1) = -3(x+1)(x-3))#

#12x-36 -10x-10 = -3(x^2-2x-3)#

#2x-46 = -3x^2+6x+9#

#3x^2-4x-55=0 " now factorise"#

#(3x+11)(x-5)=0#

If #3x+11= 0, rArr x= -11/3#

If #x-5 = rArr x = 5#