Answer:
v≈ -1.65573 ,v≈6.91725
Step-by-step explanation:
[tex]\frac{2}{v}-7+v-\frac{6}{v^2}-7v=\frac{4}{v-7}\\\mathrm{Find\:Least\:Common\:Multiplier\:of\:}v,\:v^2,\:v-7:\quad v^2\left(v-7\right)\\=\frac{2}{v}v^2\left(v-7\right)-7v^2\left(v-7\right)+vv^2\left(v-7\right)-\frac{6}{v^2}v^2\left(v-7\right)-7vv^2\left(v-7\right)=\frac{4}{v-7}v^2\left(v-7\right)\\Simplify\\=2v\left(v-7\right)-7v^2\left(v-7\right)-6v^3\left(v-7\right)-6\left(v-7\right)=4v^2\\\mathrm{Solve\:}\:2v\left(v-7\right)-7v^2\left(v-7\right)-6v^3\left(v-7\right)-6\left(v-7\right)=4v^2:\\[/tex]
[tex]v[/tex] ≈ -1.65573
[tex]v[/tex] ≈ 6.91725
v=0, v=7
