how do i solve
2q/(2q+3)-2q/(2q-3)=1
To solve the equation 2q/(2q+3) - 2q/(2q-3) = 1, you will need to follow a series of steps. Let's break it down:
Step 1: Find a common denominator for each fraction in the equation. In this case, the denominators for the two fractions are (2q+3) and (2q-3). The common denominator will be the product of these two denominators, which is (2q+3)(2q-3).
Step 2: Apply the common denominator to each fraction. Multiply the numerator and denominator of the first fraction by (2q-3), and multiply the numerator and denominator of the second fraction by (2q+3). This step will eliminate the denominators.
Step 3: Simplify both fractions by multiplying out the numerators.
The equation will now look like this:
[(2q)(2q-3)] / [(2q+3)(2q-3)] - [(2q)(2q+3)] / [(2q+3)(2q-3)] = 1
Step 4: Combine the numerators into a single fraction over the common denominator.
[4q^2 - 6q - 4q^2 - 6q] / [(2q+3)(2q-3)] = 1
Step 5: Simplify by combining like terms in the numerator.
[-12q] / [(2q+3)(2q-3)] = 1
Step 6: Multiply both sides of the equation by the [(2q+3)(2q-3)] to eliminate the fraction.
-12q = (2q+3)(2q-3)
Step 7: Expand and simplify the right side of the equation by multiplying out the terms.
-12q = 4q^2 - 9
Step 8: Bring all terms to one side of the equation to form a quadratic equation.
4q^2 - 12q - 9 = 0
At this point, the equation becomes a quadratic equation, which can be solved using factoring, the quadratic formula, or completing the square.