Solve x/frac{x{3y}+x/30}=27

$$\frac { x } { \frac { x } { 3 y } + \frac { x } { 30 } } = 27$$

Solve for x

$$x\neq 0$$

$$y=90$$

Steps for Solving Linear Equation

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3y and 30 is 30y. Multiply \frac{x}{3y} times \frac{10}{10}. Multiply \frac{x}{30} times \frac{y}{y}.

$$\frac{x}{\frac{10x}{30y}+\frac{xy}{30y}}=27$$

Since \frac{10x}{30y} and \frac{xy}{30y} have the same denominator, add them by adding their numerators.

$$\frac{x}{\frac{10x+xy}{30y}}=27$$

Divide x by \frac{10x+xy}{30y} by multiplying x by the reciprocal of \frac{10x+xy}{30y}.

$$\frac{x\times 30y}{10x+xy}=27$$

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by x\left(y+10\right).

$$x\times 30y=27x\left(y+10\right)$$

Reorder the terms.

$$30xy=27x\left(y+10\right)$$

Use the distributive property to multiply 27x by y+10.

$$30xy=27xy+270x$$

Subtract 27xy from both sides.

$$30xy-27xy=270x$$

Combine 30xy and -27xy to get 3xy.

$$3xy=270x$$

Subtract 270x from both sides.

$$3xy-270x=0$$

Combine all terms containing x.

$$\left(3y-270\right)x=0$$

Divide 0 by 3y-270.

$$x=0$$

Variable x cannot be equal to 0.

$$x\in \emptyset$$

Solve for y

$$y=90$$

$$x\neq 0$$

Steps for Solving Linear Equation

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3y and 30 is 30y. Multiply \frac{x}{3y} times \frac{10}{10}. Multiply \frac{x}{30} times \frac{y}{y}.

$$\frac{x}{\frac{10x}{30y}+\frac{xy}{30y}}=27$$

Since \frac{10x}{30y} and \frac{xy}{30y} have the same denominator, add them by adding their numerators.

$$\frac{x}{\frac{10x+xy}{30y}}=27$$

Variable y cannot be equal to 0 since division by zero is not defined. Divide x by \frac{10x+xy}{30y} by multiplying x by the reciprocal of \frac{10x+xy}{30y}.

$$\frac{x\times 30y}{10x+xy}=27$$

Factor the expressions that are not already factored in \frac{x\times 30y}{10x+xy}.

$$\frac{30xy}{x\left(y+10\right)}=27$$

Cancel out x in both numerator and denominator.

$$\frac{30y}{y+10}=27$$

Variable y cannot be equal to -10 since division by zero is not defined. Multiply both sides of the equation by y+10.

$$30y=27\left(y+10\right)$$

Use the distributive property to multiply 27 by y+10.

$$30y=27y+270$$

Subtract 27y from both sides.

$$30y-27y=270$$

Combine 30y and -27y to get 3y.

$$3y=270$$

Divide both sides by 3.

$$y=\frac{270}{3}$$

Divide 270 by 3 to get 90.

$$y=90$$