Solve F(x)=5x^2-(x+7/x^3-x

$$F ( x ) = \frac { 5 x ^ { 2 } - ( x + 7 } { x ^ { 3 } - x }$$

Solve for F

$$F=-\frac{7+x+5x^{3}-5x^{5}}{x^{2}\left(x^{2}-1\right)}$$

$$x\neq 0\text{ and }|x|\neq 1$$

Steps for Solving Linear Equation

Multiply both sides of the equation by x\left(x-1\right)\left(x+1\right).

$$Fxx\left(x-1\right)\left(x+1\right)=5x^{2}x\left(x-1\right)\left(x+1\right)-\left(x+7\right)$$

Multiply x and x to get x^{2}.

$$Fx^{2}\left(x-1\right)\left(x+1\right)=5x^{2}x\left(x-1\right)\left(x+1\right)-\left(x+7\right)$$

Use the distributive property to multiply Fx^{2} by x-1.

$$\left(Fx^{3}-Fx^{2}\right)\left(x+1\right)=5x^{2}x\left(x-1\right)\left(x+1\right)-\left(x+7\right)$$

Use the distributive property to multiply Fx^{3}-Fx^{2} by x+1 and combine like terms.

$$Fx^{4}-Fx^{2}=5x^{2}x\left(x-1\right)\left(x+1\right)-\left(x+7\right)$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$Fx^{4}-Fx^{2}=5x^{3}\left(x-1\right)\left(x+1\right)-\left(x+7\right)$$

Use the distributive property to multiply 5x^{3} by x-1.

$$Fx^{4}-Fx^{2}=\left(5x^{4}-5x^{3}\right)\left(x+1\right)-\left(x+7\right)$$

Use the distributive property to multiply 5x^{4}-5x^{3} by x+1 and combine like terms.

$$Fx^{4}-Fx^{2}=5x^{5}-5x^{3}-\left(x+7\right)$$

To find the opposite of x+7, find the opposite of each term.

$$Fx^{4}-Fx^{2}=5x^{5}-5x^{3}-x-7$$

Combine all terms containing F.

$$\left(x^{4}-x^{2}\right)F=5x^{5}-5x^{3}-x-7$$

Divide both sides by x^{4}-x^{2}.

$$\frac{\left(x^{4}-x^{2}\right)F}{x^{4}-x^{2}}=\frac{5x^{5}-5x^{3}-x-7}{x^{4}-x^{2}}$$

Dividing by x^{4}-x^{2} undoes the multiplication by x^{4}-x^{2}.

$$F=\frac{5x^{5}-5x^{3}-x-7}{x^{4}-x^{2}}$$

Divide 5x^{5}-5x^{3}-x-7 by x^{4}-x^{2}.

$$F=\frac{5x^{5}-5x^{3}-x-7}{x^{2}\left(x^{2}-1\right)}$$