Solve (a+x)(1-x)=2a-x^2

$$( a + x ) ( 1 - x ) = 2 a - x ^ { 2 }$$

Solve for a

$$a=\frac{x}{x+1}$$

$$x\neq -1$$

Steps for Solving Linear Equation

Use the distributive property to multiply a+x by 1-x.

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

Subtract 2a from both sides.

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

Combine a and -2a to get -a.

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

Subtract x from both sides.

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

Add x^{2} to both sides.

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

Combine -x^{2} and x^{2} to get 0.

$$-a-ax=-x$$

Combine all terms containing a.

$$\left(-1-x\right)a=-x$$

The equation is in standard form.

$$\left(-x-1\right)a=-x$$

Divide both sides by -x-1.

$$\frac{\left(-x-1\right)a}{-x-1}=-\frac{x}{-x-1}$$

Dividing by -x-1 undoes the multiplication by -x-1.

$$a=-\frac{x}{-x-1}$$

Divide -x by -x-1.

$$a=\frac{x}{x+1}$$

Solve for x

$$x=\frac{a}{1-a}$$

$$a\neq 1$$

Steps for Solving Linear Equation

Use the distributive property to multiply a+x by 1-x.

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

Add x^{2} to both sides.

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

Combine -x^{2} and x^{2} to get 0.

$$a-ax+x=2a$$

Subtract a from both sides.

$$-ax+x=2a-a$$

Combine 2a and -a to get a.

$$-ax+x=a$$

Combine all terms containing x.

$$\left(-a+1\right)x=a$$

The equation is in standard form.

$$\left(1-a\right)x=a$$

Divide both sides by 1-a.

$$\frac{\left(1-a\right)x}{1-a}=\frac{a}{1-a}$$

Dividing by 1-a undoes the multiplication by 1-a.

$$x=\frac{a}{1-a}$$