Solve 1/x+1/a=1

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

Solve for a

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

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

Steps for Solving Linear Equation

Variable a cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by ax, the least common multiple of x,a.

$$a+x=ax$$

Subtract ax from both sides.

$$a+x-ax=0$$

Subtract x from both sides. Anything subtracted from zero gives its negation.

$$a-ax=-x$$

Combine all terms containing a.

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

Divide both sides by 1-x.

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

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

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

Variable a cannot be equal to 0.

$$a=-\frac{x}{1-x}\text{, }a\neq 0$$

Solve for x

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

$$a\neq 0\text{ and }a\neq 1$$

Steps for Solving Linear Equation

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by ax, the least common multiple of x,a.

$$a+x=ax$$

Subtract ax from both sides.

$$a+x-ax=0$$

Subtract a from both sides. Anything subtracted from zero gives its negation.

$$x-ax=-a$$

Combine all terms containing x.

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

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.

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

Variable x cannot be equal to 0.

$$x=-\frac{a}{1-a}\text{, }x\neq 0$$