Solve 15/x+6/y=4

$$\frac{ 15 }{ x } + \frac{ 6 }{ y } =4$$

Solve for x

$$x=-\frac{15y}{2\left(3-2y\right)}$$

$$y\neq 0\text{ and }y\neq \frac{3}{2}$$

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 xy, the least common multiple of x,y.

$$y\times 15+x\times 6=4xy$$

Subtract 4xy from both sides.

$$y\times 15+x\times 6-4xy=0$$

Subtract y\times 15 from both sides. Anything subtracted from zero gives its negation.

$$x\times 6-4xy=-y\times 15$$

Multiply -1 and 15 to get -15.

$$x\times 6-4xy=-15y$$

Combine all terms containing x.

$$\left(6-4y\right)x=-15y$$

Divide both sides by -4y+6.

$$\frac{\left(6-4y\right)x}{6-4y}=-\frac{15y}{6-4y}$$

Dividing by -4y+6 undoes the multiplication by -4y+6.

$$x=-\frac{15y}{6-4y}$$

Divide -15y by -4y+6.

$$x=-\frac{15y}{2\left(3-2y\right)}$$

Variable x cannot be equal to 0.

$$x=-\frac{15y}{2\left(3-2y\right)}\text{, }x\neq 0$$

Solve for y

$$y=-\frac{6x}{15-4x}$$

$$x\neq 0\text{ and }x\neq \frac{15}{4}$$

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 xy, the least common multiple of x,y.

$$y\times 15+x\times 6=4xy$$

Subtract 4xy from both sides.

$$y\times 15+x\times 6-4xy=0$$

Subtract x\times 6 from both sides. Anything subtracted from zero gives its negation.

$$y\times 15-4xy=-x\times 6$$

Multiply -1 and 6 to get -6.

$$y\times 15-4xy=-6x$$

Combine all terms containing y.

$$\left(15-4x\right)y=-6x$$

Divide both sides by 15-4x.

$$\frac{\left(15-4x\right)y}{15-4x}=-\frac{6x}{15-4x}$$

Dividing by 15-4x undoes the multiplication by 15-4x.

$$y=-\frac{6x}{15-4x}$$

Variable y cannot be equal to 0.

$$y=-\frac{6x}{15-4x}\text{, }y\neq 0$$