How do you solve (2q)/(2q+3)-(2q)/(2q-3)=1?

1 Answer
Nov 27, 2016

We should find a common denominator of (2q+3)(2q-3).

(2q(2q-3))/((2q+3)(2q-3))-(2q(2q+3))/((2q+3)(2q-3))=((2q+3)(2q-3))/((2q+3)(2q-3))

Combining:

(2q(2q-3)-2q(2q+3))/(4q^2-9)=(4q^2-9)/(4q^2-9)

Multiplying through and disregarding the denominator since they're all equal:

(4q^2-6q)-(4q^2+6q)=4q^2-9

Pay attention to positives and negatives here:

-12q=4q^2-9

4q^2+12q-9=0

Using the Quadratic Formula:

q=(-b+-sqrt(b^2-4ac))/(2a)=(-12+-sqrt(144+144))/8

q=(-12+-12sqrt2)/8=(-3+-3sqrt2)/4