Solve 6/x-1-3/y-2=1

$$\frac { 6 } { x - 1 } - \frac { 3 } { y - 2 } = 1$$

Solve for x

$$x=-\frac{11-7y}{y+1}$$

$$y\neq 2\text{ and }y\neq -1$$

Steps for Solving Linear Equation

Variable x cannot be equal to 1 since division by zero is not defined. Multiply both sides of the equation by \left(x-1\right)\left(y-2\right), the least common multiple of x-1,y-2.

$$\left(y-2\right)\times 6-\left(x-1\right)\times 3=\left(x-1\right)\left(y-2\right)$$

Use the distributive property to multiply y-2 by 6.

$$6y-12-\left(x-1\right)\times 3=\left(x-1\right)\left(y-2\right)$$

Use the distributive property to multiply x-1 by 3.

$$6y-12-\left(3x-3\right)=\left(x-1\right)\left(y-2\right)$$

To find the opposite of 3x-3, find the opposite of each term.

$$6y-12-3x+3=\left(x-1\right)\left(y-2\right)$$

Add -12 and 3 to get -9.

$$6y-9-3x=\left(x-1\right)\left(y-2\right)$$

Use the distributive property to multiply x-1 by y-2.

$$6y-9-3x=xy-2x-y+2$$

Subtract xy from both sides.

$$6y-9-3x-xy=-2x-y+2$$

Add 2x to both sides.

$$6y-9-3x-xy+2x=-y+2$$

Combine -3x and 2x to get -x.

$$6y-9-x-xy=-y+2$$

Subtract 6y from both sides.

$$-9-x-xy=-y+2-6y$$

Combine -y and -6y to get -7y.

$$-9-x-xy=-7y+2$$

Add 9 to both sides.

$$-x-xy=-7y+2+9$$

Add 2 and 9 to get 11.

$$-x-xy=-7y+11$$

Combine all terms containing x.

$$\left(-1-y\right)x=-7y+11$$

The equation is in standard form.

$$\left(-y-1\right)x=11-7y$$

Divide both sides by -y-1.

$$\frac{\left(-y-1\right)x}{-y-1}=\frac{11-7y}{-y-1}$$

Dividing by -y-1 undoes the multiplication by -y-1.

$$x=\frac{11-7y}{-y-1}$$

Divide -7y+11 by -y-1.

$$x=-\frac{11-7y}{y+1}$$

Variable x cannot be equal to 1.

$$x=-\frac{11-7y}{y+1}\text{, }x\neq 1$$

Solve for y

$$y=\frac{x+11}{7-x}$$

$$x\neq 1\text{ and }x\neq 7$$

Steps for Solving Linear Equation

Variable y cannot be equal to 2 since division by zero is not defined. Multiply both sides of the equation by \left(x-1\right)\left(y-2\right), the least common multiple of x-1,y-2.

$$\left(y-2\right)\times 6-\left(x-1\right)\times 3=\left(x-1\right)\left(y-2\right)$$

Use the distributive property to multiply y-2 by 6.

$$6y-12-\left(x-1\right)\times 3=\left(x-1\right)\left(y-2\right)$$

Use the distributive property to multiply x-1 by 3.

$$6y-12-\left(3x-3\right)=\left(x-1\right)\left(y-2\right)$$

To find the opposite of 3x-3, find the opposite of each term.

$$6y-12-3x+3=\left(x-1\right)\left(y-2\right)$$

Add -12 and 3 to get -9.

$$6y-9-3x=\left(x-1\right)\left(y-2\right)$$

Use the distributive property to multiply x-1 by y-2.

$$6y-9-3x=xy-2x-y+2$$

Subtract xy from both sides.

$$6y-9-3x-xy=-2x-y+2$$

Add y to both sides.

$$6y-9-3x-xy+y=-2x+2$$

Combine 6y and y to get 7y.

$$7y-9-3x-xy=-2x+2$$

Add 9 to both sides.

$$7y-3x-xy=-2x+2+9$$

Add 2 and 9 to get 11.

$$7y-3x-xy=-2x+11$$

Add 3x to both sides.

$$7y-xy=-2x+11+3x$$

Combine -2x and 3x to get x.

$$7y-xy=x+11$$

Combine all terms containing y.

$$\left(7-x\right)y=x+11$$

Divide both sides by -x+7.

$$\frac{\left(7-x\right)y}{7-x}=\frac{x+11}{7-x}$$

Dividing by -x+7 undoes the multiplication by -x+7.

$$y=\frac{x+11}{7-x}$$

Variable y cannot be equal to 2.

$$y=\frac{x+11}{7-x}\text{, }y\neq 2$$