Solve x-4/a=x+3/b

$$\frac { x - 4 } { a } = \frac { x + 3 } { b }$$

Solve for a

$$a=\frac{b\left(x-4\right)}{x+3}$$

$$x\neq 4\text{ and }b\neq 0\text{ and }x\neq -3$$

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 ab, the least common multiple of a,b.

$$b\left(x-4\right)=a\left(x+3\right)$$

Use the distributive property to multiply b by x-4.

$$bx-4b=a\left(x+3\right)$$

Use the distributive property to multiply a by x+3.

$$bx-4b=ax+3a$$

Swap sides so that all variable terms are on the left hand side.

$$ax+3a=bx-4b$$

Combine all terms containing a.

$$\left(x+3\right)a=bx-4b$$

Divide both sides by x+3.

$$\frac{\left(x+3\right)a}{x+3}=\frac{b\left(x-4\right)}{x+3}$$

Dividing by x+3 undoes the multiplication by x+3.

$$a=\frac{b\left(x-4\right)}{x+3}$$

Variable a cannot be equal to 0.

$$a=\frac{b\left(x-4\right)}{x+3}\text{, }a\neq 0$$

Solve for b

$$b=-\frac{a\left(x+3\right)}{4-x}$$

$$x\neq -3\text{ and }a\neq 0\text{ and }x\neq 4$$

Steps for Solving Linear Equation

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

$$b\left(x-4\right)=a\left(x+3\right)$$

Use the distributive property to multiply b by x-4.

$$bx-4b=a\left(x+3\right)$$

Use the distributive property to multiply a by x+3.

$$bx-4b=ax+3a$$

Combine all terms containing b.

$$\left(x-4\right)b=ax+3a$$

Divide both sides by x-4.

$$\frac{\left(x-4\right)b}{x-4}=\frac{a\left(x+3\right)}{x-4}$$

Dividing by x-4 undoes the multiplication by x-4.

$$b=\frac{a\left(x+3\right)}{x-4}$$

Variable b cannot be equal to 0.

$$b=\frac{a\left(x+3\right)}{x-4}\text{, }b\neq 0$$