What is the answer to 8/q+2=(q+4)/(q-1) ?

The answer to 8/q+2=(q+4)/(q-1) is q=2,q=-4

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8/q+2=(q+4)/(q-1)

\frac{8}{q} + 2 = \frac{q + 4}{q - 1}

q = 2, q = - 4

Solution steps

\frac{8}{q} + 2 = \frac{q + 4}{q - 1}

Multiply by LCM

8 (q - 1) + 2 q (q - 1) = q (q + 4)

Solve

8 (q - 1) + 2 q (q - 1) = q (q + 4) : q = 2, q = - 4

q = 2, q = - 4

Verify Solutions

Find undefined (singularity) points:

q = 0, q = 1

Combine undefined points with solutions:

q = 2, q = - 4

\frac{1}{8} + \frac{1}{x} = \frac{1}{2}

2 x + \frac{16}{x ^{2}} = 0

0 = 1 - \frac{9}{x ^{2}}

3 - \frac{2}{x + 4} = - \frac{2 x}{x + 4}

\frac{3}{2} + \frac{1}{3} = \frac{1}{x}

What is the answer to 8/q+2=(q+4)/(q-1) ?
The answer to 8/q+2=(q+4)/(q-1) is q=2,q=-4
Solve for q: 8/q+2=(q+4)/(q-1)
The solution is q=2,q=-4