Solve 2-7u/1-5u=3+7u/4+5v

$$\frac { 2 - 7 u } { 1 - 5 u } = \frac { 3 + 7 u } { 4 + 5 v }$$

Solve for v

$$v=-\frac{7u^{2}-4u+1}{2-7u}$$

$$u\neq -\frac{3}{7}\text{ and }u\neq \frac{1}{5}\text{ and }u\neq \frac{2}{7}$$

Steps for Solving Linear Equation

Variable v cannot be equal to -\frac{4}{5} since division by zero is not defined. Multiply both sides of the equation by \left(5u-1\right)\left(5v+4\right), the least common multiple of 1-5u,4+5v.

$$\left(-4-5v\right)\left(2-7u\right)=\left(5u-1\right)\left(3+7u\right)$$

Use the distributive property to multiply -4-5v by 2-7u.

$$-8+28u-10v+35vu=\left(5u-1\right)\left(3+7u\right)$$

Use the distributive property to multiply 5u-1 by 3+7u and combine like terms.

$$-8+28u-10v+35vu=8u+35u^{2}-3$$

Add 8 to both sides.

$$28u-10v+35vu=8u+35u^{2}-3+8$$

Add -3 and 8 to get 5.

$$28u-10v+35vu=8u+35u^{2}+5$$

Subtract 28u from both sides.

$$-10v+35vu=8u+35u^{2}+5-28u$$

Combine 8u and -28u to get -20u.

$$-10v+35vu=-20u+35u^{2}+5$$

Combine all terms containing v.

$$\left(-10+35u\right)v=-20u+35u^{2}+5$$

The equation is in standard form.

$$\left(35u-10\right)v=35u^{2}-20u+5$$

Divide both sides by -10+35u.

$$\frac{\left(35u-10\right)v}{35u-10}=\frac{35u^{2}-20u+5}{35u-10}$$

Dividing by -10+35u undoes the multiplication by -10+35u.

$$v=\frac{35u^{2}-20u+5}{35u-10}$$

Divide -20u+35u^{2}+5 by -10+35u.

$$v=\frac{7u^{2}-4u+1}{7u-2}$$

Variable v cannot be equal to -\frac{4}{5}.

$$v=\frac{7u^{2}-4u+1}{7u-2}\text{, }v\neq -\frac{4}{5}$$

Solve for u

$$u=\frac{\sqrt{49v^{2}-12}}{14}+\frac{v}{2}+\frac{2}{7}$$

$$u=-\frac{\sqrt{49v^{2}-12}}{14}+\frac{v}{2}+\frac{2}{7}\text{, }\left(v\leq -\frac{2\sqrt{3}}{7}\text{ and }v\neq -\frac{4}{5}\right)\text{ or }v\geq \frac{2\sqrt{3}}{7}$$