Solve 25/x-7+5/3=24-1/x

$$\frac{ 25 }{ x } -7+ \frac{ 5 }{ 3 } = 24- \frac{ 1 }{ x }$$

Solve for x

$$x=\frac{39}{44}\approx 0.886363636$$

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 3x, the least common multiple of x,3.

$$3\times 25+3x\left(-7\right)+3x\times \frac{5}{3}=3x\times 24-3$$

Multiply 3 and 25 to get 75.

$$75+3x\left(-7\right)+3x\times \frac{5}{3}=3x\times 24-3$$

Multiply 3 and -7 to get -21.

$$75-21x+3x\times \frac{5}{3}=3x\times 24-3$$

Cancel out 3 and 3.

$$75-21x+5x=3x\times 24-3$$

Combine -21x and 5x to get -16x.

$$75-16x=3x\times 24-3$$

Multiply 3 and 24 to get 72.

$$75-16x=72x-3$$

Subtract 72x from both sides.

$$75-16x-72x=-3$$

Combine -16x and -72x to get -88x.

$$75-88x=-3$$

Subtract 75 from both sides.

$$-88x=-3-75$$

Subtract 75 from -3 to get -78.

$$-88x=-78$$

Divide both sides by -88.

$$x=\frac{-78}{-88}$$

Reduce the fraction \frac{-78}{-88} to lowest terms by extracting and canceling out -2.

$$x=\frac{39}{44}$$