Solve 4/2x-7=3/x

$$\frac{ 4 }{ 2x-7 } = \frac{ 3 }{ x }$$

Solve for x

$$x = \frac{21}{2} = 10\frac{1}{2} = 10.5$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values 0,\frac{7}{2} since division by zero is not defined. Multiply both sides of the equation by x\left(2x-7\right), the least common multiple of 2x-7,x.

$$x\times 4=\left(2x-7\right)\times 3$$

Use the distributive property to multiply 2x-7 by 3.

$$x\times 4=6x-21$$

Subtract 6x from both sides.

$$x\times 4-6x=-21$$

Combine x\times 4 and -6x to get -2x.

$$-2x=-21$$

Divide both sides by -2.

$$x=\frac{-21}{-2}$$

Fraction \frac{-21}{-2} can be simplified to \frac{21}{2} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{21}{2}$$