Solve 150x/y(5+x)=5+10x/5+x

$$\frac { 150 x } { y ( 5 + x ) } = 5 + \frac { 10 x } { 5 + x }$$

Solve for x

$$x=\frac{5y}{3\left(10-y\right)}$$

$$y\neq 15\text{ and }y\neq 10\text{ and }y\neq 0$$

Steps for Solving Linear Equation

Variable x cannot be equal to -5 since division by zero is not defined. Multiply both sides of the equation by y\left(x+5\right), the least common multiple of y\left(5+x\right),5+x.

$$150x=y\left(x+5\right)\times 5+y\times 10x$$

Use the distributive property to multiply y by x+5.

$$150x=\left(yx+5y\right)\times 5+y\times 10x$$

Use the distributive property to multiply yx+5y by 5.

$$150x=5yx+25y+y\times 10x$$

Combine 5yx and y\times 10x to get 15yx.

$$150x=15yx+25y$$

Subtract 15yx from both sides.

$$150x-15yx=25y$$

Combine all terms containing x.

$$\left(150-15y\right)x=25y$$

Divide both sides by 150-15y.

$$\frac{\left(150-15y\right)x}{150-15y}=\frac{25y}{150-15y}$$

Dividing by 150-15y undoes the multiplication by 150-15y.

$$x=\frac{25y}{150-15y}$$

Divide 25y by 150-15y.

$$x=\frac{5y}{3\left(10-y\right)}$$

Variable x cannot be equal to -5.

$$x=\frac{5y}{3\left(10-y\right)}\text{, }x\neq -5$$

Solve for y

$$y=\frac{30x}{3x+5}$$

$$x\neq 0\text{ and }x\neq -\frac{5}{3}\text{ and }x\neq -5$$

Steps for Solving Linear Equation

Variable y cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by y\left(x+5\right), the least common multiple of y\left(5+x\right),5+x.

$$150x=y\left(x+5\right)\times 5+y\times 10x$$

Use the distributive property to multiply y by x+5.

$$150x=\left(yx+5y\right)\times 5+y\times 10x$$

Use the distributive property to multiply yx+5y by 5.

$$150x=5yx+25y+y\times 10x$$

Combine 5yx and y\times 10x to get 15yx.

$$150x=15yx+25y$$

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

$$15yx+25y=150x$$

Combine all terms containing y.

$$\left(15x+25\right)y=150x$$

Divide both sides by 15x+25.

$$\frac{\left(15x+25\right)y}{15x+25}=\frac{150x}{15x+25}$$

Dividing by 15x+25 undoes the multiplication by 15x+25.

$$y=\frac{150x}{15x+25}$$

Divide 150x by 15x+25.

$$y=\frac{30x}{3x+5}$$

Variable y cannot be equal to 0.

$$y=\frac{30x}{3x+5}\text{, }y\neq 0$$