Solve 3/x+4/y-5=10

$$\frac{ 3 }{ x } + \frac{ 4 }{ y-5 } = 10$$

Solve for x

$$x=-\frac{3\left(y-5\right)}{2\left(27-5y\right)}$$

$$y\neq 5\text{ and }y\neq \frac{27}{5}$$

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 x\left(y-5\right), the least common multiple of x,y-5.

$$\left(y-5\right)\times 3+x\times 4=10x\left(y-5\right)$$

Use the distributive property to multiply y-5 by 3.

$$3y-15+x\times 4=10x\left(y-5\right)$$

Use the distributive property to multiply 10x by y-5.

$$3y-15+x\times 4=10xy-50x$$

Subtract 10xy from both sides.

$$3y-15+x\times 4-10xy=-50x$$

Add 50x to both sides.

$$3y-15+x\times 4-10xy+50x=0$$

Combine x\times 4 and 50x to get 54x.

$$3y-15+54x-10xy=0$$

Subtract 3y from both sides. Anything subtracted from zero gives its negation.

$$-15+54x-10xy=-3y$$

Add 15 to both sides.

$$54x-10xy=-3y+15$$

Combine all terms containing x.

$$\left(54-10y\right)x=-3y+15$$

The equation is in standard form.

$$\left(54-10y\right)x=15-3y$$

Divide both sides by -10y+54.

$$\frac{\left(54-10y\right)x}{54-10y}=\frac{15-3y}{54-10y}$$

Dividing by -10y+54 undoes the multiplication by -10y+54.

$$x=\frac{15-3y}{54-10y}$$

Divide -3y+15 by -10y+54.

$$x=\frac{3\left(5-y\right)}{2\left(27-5y\right)}$$

Variable x cannot be equal to 0.

$$x=\frac{3\left(5-y\right)}{2\left(27-5y\right)}\text{, }x\neq 0$$

Solve for y

$$y=-\frac{3\left(18x-5\right)}{3-10x}$$

$$x\neq 0\text{ and }x\neq \frac{3}{10}$$

Steps for Solving Linear Equation

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

$$\left(y-5\right)\times 3+x\times 4=10x\left(y-5\right)$$

Use the distributive property to multiply y-5 by 3.

$$3y-15+x\times 4=10x\left(y-5\right)$$

Use the distributive property to multiply 10x by y-5.

$$3y-15+x\times 4=10xy-50x$$

Subtract 10xy from both sides.

$$3y-15+x\times 4-10xy=-50x$$

Add 15 to both sides.

$$3y+x\times 4-10xy=-50x+15$$

Subtract x\times 4 from both sides.

$$3y-10xy=-50x+15-x\times 4$$

Combine -50x and -x\times 4 to get -54x.

$$3y-10xy=-54x+15$$

Combine all terms containing y.

$$\left(3-10x\right)y=-54x+15$$

The equation is in standard form.

$$\left(3-10x\right)y=15-54x$$

Divide both sides by 3-10x.

$$\frac{\left(3-10x\right)y}{3-10x}=\frac{15-54x}{3-10x}$$

Dividing by 3-10x undoes the multiplication by 3-10x.

$$y=\frac{15-54x}{3-10x}$$

Divide 15-54x by 3-10x.

$$y=\frac{3\left(5-18x\right)}{3-10x}$$

Variable y cannot be equal to 5.

$$y=\frac{3\left(5-18x\right)}{3-10x}\text{, }y\neq 5$$