How do you solve #\frac{3x^2+2x-1}{x^2-1}=-2# using cross multiplication?
1 Answer
Dec 11, 2014
Step 1
Make the right side of the equation a fraction:
#\frac{3x^2+2x-1}{x^2-1}=-2/1#
Step 2
Cross multiply:
#-1(3x^2+2x-1) = -2(x^2 - 1)#
#-3x^2 - 2x + 1 = -2x^2 + 2#
Step 3
Simplify:
#-2x +1 = -2x^2 + 3x^2 + 2#
#-2x + 1 = x^2 + 2#
#-2x = x^2 + 1#
#0 = x^2 + 2x + 1#
Step 4
Solve for
#0 = x^2 + 2x + 1#
We notice that the above represents the expanded form of the perfect square:
#0 = (x + 1)^2#
Because of the perfect square, we know that x has only one value:
#x = -1#