Solve x^2-14n+49/x^2-49=3/17

$$\frac { x ^ { 2 } - 14 n + 49 } { x ^ { 2 } - 49 } = \frac { 3 } { 17 }$$

Solve for n (complex solution)

$$n=\frac{x^{2}+70}{17}$$

$$x\neq -7\text{ and }x\neq 7$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 17\left(x-7\right)\left(x+7\right), the least common multiple of x^{2}-49,17.

$$17\left(x^{2}-14n+49\right)=3\left(x-7\right)\left(x+7\right)$$

Use the distributive property to multiply 17 by x^{2}-14n+49.

$$17x^{2}-238n+833=3\left(x-7\right)\left(x+7\right)$$

Use the distributive property to multiply 3 by x-7.

$$17x^{2}-238n+833=\left(3x-21\right)\left(x+7\right)$$

Use the distributive property to multiply 3x-21 by x+7 and combine like terms.

$$17x^{2}-238n+833=3x^{2}-147$$

Subtract 17x^{2} from both sides.

$$-238n+833=3x^{2}-147-17x^{2}$$

Combine 3x^{2} and -17x^{2} to get -14x^{2}.

$$-238n+833=-14x^{2}-147$$

Subtract 833 from both sides.

$$-238n=-14x^{2}-147-833$$

Subtract 833 from -147 to get -980.

$$-238n=-14x^{2}-980$$

Divide both sides by -238.

$$\frac{-238n}{-238}=\frac{-14x^{2}-980}{-238}$$

Dividing by -238 undoes the multiplication by -238.

$$n=\frac{-14x^{2}-980}{-238}$$

Divide -14x^{2}-980 by -238.

$$n=\frac{x^{2}+70}{17}$$

Solve for n

$$n=\frac{x^{2}+70}{17}$$

$$|x|\neq 7$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 17\left(x-7\right)\left(x+7\right), the least common multiple of x^{2}-49,17.

$$17\left(x^{2}-14n+49\right)=3\left(x-7\right)\left(x+7\right)$$

Use the distributive property to multiply 17 by x^{2}-14n+49.

$$17x^{2}-238n+833=3\left(x-7\right)\left(x+7\right)$$

Use the distributive property to multiply 3 by x-7.

$$17x^{2}-238n+833=\left(3x-21\right)\left(x+7\right)$$

Use the distributive property to multiply 3x-21 by x+7 and combine like terms.

$$17x^{2}-238n+833=3x^{2}-147$$

Subtract 17x^{2} from both sides.

$$-238n+833=3x^{2}-147-17x^{2}$$

Combine 3x^{2} and -17x^{2} to get -14x^{2}.

$$-238n+833=-14x^{2}-147$$

Subtract 833 from both sides.

$$-238n=-14x^{2}-147-833$$

Subtract 833 from -147 to get -980.

$$-238n=-14x^{2}-980$$

Divide both sides by -238.

$$\frac{-238n}{-238}=\frac{-14x^{2}-980}{-238}$$

Dividing by -238 undoes the multiplication by -238.

$$n=\frac{-14x^{2}-980}{-238}$$

Divide -14x^{2}-980 by -238.

$$n=\frac{x^{2}+70}{17}$$

Solve for x (complex solution)

$$x=-\sqrt{17n-70}$$

$$x=\sqrt{17n-70}\text{, }n\neq 7$$

Solve for x

$$x=\sqrt{17n-70}$$

$$x=-\sqrt{17n-70}\text{, }n\neq 7\text{ and }n\geq \frac{70}{17}$$