Solve 1/u-3+1/x=11/4

$$\frac { 1 } { u - 3 } + \frac { 1 } { x } = 1 \frac { 1 } { 4 }$$

Solve for u

$$u=-\frac{19x-12}{4-5x}$$

$$x\neq 0\text{ and }x\neq \frac{4}{5}$$

Steps for Solving Linear Equation

Variable u cannot be equal to 3 since division by zero is not defined. Multiply both sides of the equation by 4x\left(u-3\right), the least common multiple of u-3,x,4.

$$4x+4u-12=x\left(u-3\right)\left(1\times 4+1\right)$$

Multiply 1 and 4 to get 4.

$$4x+4u-12=x\left(u-3\right)\left(4+1\right)$$

Add 4 and 1 to get 5.

$$4x+4u-12=x\left(u-3\right)\times 5$$

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

$$4x+4u-12=\left(xu-3x\right)\times 5$$

Use the distributive property to multiply xu-3x by 5.

$$4x+4u-12=5xu-15x$$

Subtract 5xu from both sides.

$$4x+4u-12-5xu=-15x$$

Subtract 4x from both sides.

$$4u-12-5xu=-15x-4x$$

Combine -15x and -4x to get -19x.

$$4u-12-5xu=-19x$$

Add 12 to both sides.

$$4u-5xu=-19x+12$$

Combine all terms containing u.

$$\left(4-5x\right)u=-19x+12$$

The equation is in standard form.

$$\left(4-5x\right)u=12-19x$$

Divide both sides by 4-5x.

$$\frac{\left(4-5x\right)u}{4-5x}=\frac{12-19x}{4-5x}$$

Dividing by 4-5x undoes the multiplication by 4-5x.

$$u=\frac{12-19x}{4-5x}$$

Variable u cannot be equal to 3.

$$u=\frac{12-19x}{4-5x}\text{, }u\neq 3$$

Solve for x

$$x=-\frac{4\left(u-3\right)}{19-5u}$$

$$u\neq 3\text{ and }u\neq \frac{19}{5}$$

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 4x\left(u-3\right), the least common multiple of u-3,x,4.

$$4x+4u-12=x\left(u-3\right)\left(1\times 4+1\right)$$

Multiply 1 and 4 to get 4.

$$4x+4u-12=x\left(u-3\right)\left(4+1\right)$$

Add 4 and 1 to get 5.

$$4x+4u-12=x\left(u-3\right)\times 5$$

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

$$4x+4u-12=\left(xu-3x\right)\times 5$$

Use the distributive property to multiply xu-3x by 5.

$$4x+4u-12=5xu-15x$$

Subtract 5xu from both sides.

$$4x+4u-12-5xu=-15x$$

Add 15x to both sides.

$$4x+4u-12-5xu+15x=0$$

Combine 4x and 15x to get 19x.

$$19x+4u-12-5xu=0$$

Subtract 4u from both sides. Anything subtracted from zero gives its negation.

$$19x-12-5xu=-4u$$

Add 12 to both sides.

$$19x-5xu=-4u+12$$

Combine all terms containing x.

$$\left(19-5u\right)x=-4u+12$$

The equation is in standard form.

$$\left(19-5u\right)x=12-4u$$

Divide both sides by 19-5u.

$$\frac{\left(19-5u\right)x}{19-5u}=\frac{12-4u}{19-5u}$$

Dividing by 19-5u undoes the multiplication by 19-5u.

$$x=\frac{12-4u}{19-5u}$$

Divide 12-4u by 19-5u.

$$x=\frac{4\left(3-u\right)}{19-5u}$$

Variable x cannot be equal to 0.

$$x=\frac{4\left(3-u\right)}{19-5u}\text{, }x\neq 0$$