Solve 30/a*b=x(y-z)

$$\frac { 30 } { a \cdot b } = x ( y - z )$$

Solve for a

$$a=-\frac{30}{bx\left(z-y\right)}$$

$$y\neq z\text{ and }x\neq 0\text{ and }b\neq 0$$

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.

$$30=x\left(y-z\right)ab$$

Use the distributive property to multiply x by y-z.

$$30=\left(xy-xz\right)ab$$

Use the distributive property to multiply xy-xz by a.

$$30=\left(xya-xza\right)b$$

Use the distributive property to multiply xya-xza by b.

$$30=xyab-xzab$$

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

$$xyab-xzab=30$$

Combine all terms containing a.

$$\left(xyb-xzb\right)a=30$$

The equation is in standard form.

$$\left(bxy-bxz\right)a=30$$

Divide both sides by xyb-xzb.

$$\frac{\left(bxy-bxz\right)a}{bxy-bxz}=\frac{30}{bxy-bxz}$$

Dividing by xyb-xzb undoes the multiplication by xyb-xzb.

$$a=\frac{30}{bxy-bxz}$$

Divide 30 by xyb-xzb.

$$a=\frac{30}{bx\left(y-z\right)}$$

Variable a cannot be equal to 0.

$$a=\frac{30}{bx\left(y-z\right)}\text{, }a\neq 0$$

Solve for b

$$b=-\frac{30}{ax\left(z-y\right)}$$

$$y\neq z\text{ and }x\neq 0\text{ and }a\neq 0$$

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.

$$30=x\left(y-z\right)ab$$

Use the distributive property to multiply x by y-z.

$$30=\left(xy-xz\right)ab$$

Use the distributive property to multiply xy-xz by a.

$$30=\left(xya-xza\right)b$$

Use the distributive property to multiply xya-xza by b.

$$30=xyab-xzab$$

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

$$xyab-xzab=30$$

Combine all terms containing b.

$$\left(xya-xza\right)b=30$$

The equation is in standard form.

$$\left(axy-axz\right)b=30$$

Divide both sides by xya-xza.

$$\frac{\left(axy-axz\right)b}{axy-axz}=\frac{30}{axy-axz}$$

Dividing by xya-xza undoes the multiplication by xya-xza.

$$b=\frac{30}{axy-axz}$$

Divide 30 by xya-xza.

$$b=\frac{30}{ax\left(y-z\right)}$$

Variable b cannot be equal to 0.

$$b=\frac{30}{ax\left(y-z\right)}\text{, }b\neq 0$$