Solve x^2(a-b)=(a+b)

$$x ^ { 2 } ( a - b ) = ( a + b )$$

Solve for a

$$\left\{\begin{matrix}a=\frac{b\left(x^{2}+1\right)}{x^{2}-1}\text{, }&|x|\neq 1\\a\in \mathrm{R}\text{, }&b=0\text{ and }|x|=1\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply x^{2} by a-b.

$$x^{2}a-x^{2}b=a+b$$

Subtract a from both sides.

$$x^{2}a-x^{2}b-a=b$$

Add x^{2}b to both sides.

$$x^{2}a-a=b+x^{2}b$$

Combine all terms containing a.

$$\left(x^{2}-1\right)a=b+x^{2}b$$

The equation is in standard form.

$$\left(x^{2}-1\right)a=bx^{2}+b$$

Divide both sides by x^{2}-1.

$$\frac{\left(x^{2}-1\right)a}{x^{2}-1}=\frac{bx^{2}+b}{x^{2}-1}$$

Dividing by x^{2}-1 undoes the multiplication by x^{2}-1.

$$a=\frac{bx^{2}+b}{x^{2}-1}$$

Divide b+bx^{2} by x^{2}-1.

$$a=\frac{b\left(x^{2}+1\right)}{x^{2}-1}$$

Solve for b

$$b=\frac{a\left(x^{2}-1\right)}{x^{2}+1}$$

Steps for Solving Linear Equation

Use the distributive property to multiply x^{2} by a-b.

$$x^{2}a-x^{2}b=a+b$$

Subtract b from both sides.

$$x^{2}a-x^{2}b-b=a$$

Subtract x^{2}a from both sides.

$$-x^{2}b-b=a-x^{2}a$$

Reorder the terms.

$$-bx^{2}-b=-ax^{2}+a$$

Combine all terms containing b.

$$\left(-x^{2}-1\right)b=-ax^{2}+a$$

The equation is in standard form.

$$\left(-x^{2}-1\right)b=a-ax^{2}$$

Divide both sides by -x^{2}-1.

$$\frac{\left(-x^{2}-1\right)b}{-x^{2}-1}=\frac{a-ax^{2}}{-x^{2}-1}$$

Dividing by -x^{2}-1 undoes the multiplication by -x^{2}-1.

$$b=\frac{a-ax^{2}}{-x^{2}-1}$$

Divide a-ax^{2} by -x^{2}-1.

$$b=-\frac{a\left(1-x^{2}\right)}{x^{2}+1}$$