The solution set of the equation is {-4, 2}
Given expression:
[tex]\frac{8}{q} +2=\frac{q+4}{q-1}[/tex]
Solve for q: simplify
[tex]\frac{8}{q} +2=\frac{q+4}{q-1}\\\frac{8+2q}{q}=\frac{q+4}{q-1}\\(8+2q)(q-1)=(q(q+4)\\8q-8+2q^{2} -2q=q^{2} +4q\\2q^{2} +6q-8 =q^{2}+4q\\q^{2} +2q-8=0[/tex]
Factorize the quadratic equation to solve q
[tex]q^{2} +4q-2q-8=0\\q(q+4)-2(q+4)=0\\(q+4)=0, (q-2)=0\\q= -4, 2[/tex]
Therefore, The solution set of the equation is {-4, 2}
For more information:
https://brainly.com/question/12703606
