Solve n5/x-3-x+5/(x-3)(x+2)=7/x+2

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

Solve for n

$$n=-\frac{8\left(2-x\right)}{5\left(x+2\right)}$$

$$x\neq 3\text{ and }x\neq -2$$

Steps for Solving Linear Equation

Multiply both sides of the equation by \left(x-3\right)\left(x+2\right), the least common multiple of x-3,\left(x-3\right)\left(x+2\right),x+2.

$$n\left(x+2\right)\times 5-\left(x+5\right)=\left(x-3\right)\times 7$$

Use the distributive property to multiply n by x+2.

$$\left(nx+2n\right)\times 5-\left(x+5\right)=\left(x-3\right)\times 7$$

Use the distributive property to multiply nx+2n by 5.

$$5nx+10n-\left(x+5\right)=\left(x-3\right)\times 7$$

To find the opposite of x+5, find the opposite of each term.

$$5nx+10n-x-5=\left(x-3\right)\times 7$$

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

$$5nx+10n-x-5=7x-21$$

Add x to both sides.

$$5nx+10n-5=7x-21+x$$

Combine 7x and x to get 8x.

$$5nx+10n-5=8x-21$$

Add 5 to both sides.

$$5nx+10n=8x-21+5$$

Add -21 and 5 to get -16.

$$5nx+10n=8x-16$$

Combine all terms containing n.

$$\left(5x+10\right)n=8x-16$$

Divide both sides by 5x+10.

$$\frac{\left(5x+10\right)n}{5x+10}=\frac{8x-16}{5x+10}$$

Dividing by 5x+10 undoes the multiplication by 5x+10.

$$n=\frac{8x-16}{5x+10}$$

Divide -16+8x by 5x+10.

$$n=\frac{8\left(x-2\right)}{5\left(x+2\right)}$$

Solve for x

$$x=-\frac{2\left(5n+8\right)}{5n-8}$$

$$n\neq \frac{8}{25}\text{ and }n\neq \frac{8}{5}$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -2,3 since division by zero is not defined. Multiply both sides of the equation by \left(x-3\right)\left(x+2\right), the least common multiple of x-3,\left(x-3\right)\left(x+2\right),x+2.

$$n\left(x+2\right)\times 5-\left(x+5\right)=\left(x-3\right)\times 7$$

Use the distributive property to multiply n by x+2.

$$\left(nx+2n\right)\times 5-\left(x+5\right)=\left(x-3\right)\times 7$$

Use the distributive property to multiply nx+2n by 5.

$$5nx+10n-\left(x+5\right)=\left(x-3\right)\times 7$$

To find the opposite of x+5, find the opposite of each term.

$$5nx+10n-x-5=\left(x-3\right)\times 7$$

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

$$5nx+10n-x-5=7x-21$$

Subtract 7x from both sides.

$$5nx+10n-x-5-7x=-21$$

Combine -x and -7x to get -8x.

$$5nx+10n-8x-5=-21$$

Subtract 10n from both sides.

$$5nx-8x-5=-21-10n$$

Add 5 to both sides.

$$5nx-8x=-21-10n+5$$

Add -21 and 5 to get -16.

$$5nx-8x=-16-10n$$

Combine all terms containing x.

$$\left(5n-8\right)x=-16-10n$$

The equation is in standard form.

$$\left(5n-8\right)x=-10n-16$$

Divide both sides by 5n-8.

$$\frac{\left(5n-8\right)x}{5n-8}=\frac{-10n-16}{5n-8}$$

Dividing by 5n-8 undoes the multiplication by 5n-8.

$$x=\frac{-10n-16}{5n-8}$$

Divide -16-10n by 5n-8.

$$x=-\frac{2\left(5n+8\right)}{5n-8}$$

Variable x cannot be equal to any of the values -2,3.

$$x=-\frac{2\left(5n+8\right)}{5n-8}\text{, }x\neq -2\text{ and }x\neq 3$$