Solve 2x+5/x-3=1/3+4/x-3

$$\frac{ 2x+5 }{ x-3 } = \frac{ 1 }{ 3 } + \frac{ 4 }{ x-3 }$$

Solve for x

$$x = -\frac{6}{5} = -1\frac{1}{5} = -1.2$$

Steps for Solving Linear Equation

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

$$3\left(2x+5\right)=3\left(x-3\right)\times \frac{1}{3}+3\times 4$$

Use the distributive property to multiply 3 by 2x+5.

$$6x+15=3\left(x-3\right)\times \frac{1}{3}+3\times 4$$

Multiply 3 and \frac{1}{3} to get 1.

$$6x+15=x-3+3\times 4$$

Multiply 3 and 4 to get 12.

$$6x+15=x-3+12$$

Add -3 and 12 to get 9.

$$6x+15=x+9$$

Subtract x from both sides.

$$6x+15-x=9$$

Combine 6x and -x to get 5x.

$$5x+15=9$$

Subtract 15 from both sides.

$$5x=9-15$$

Subtract 15 from 9 to get -6.

$$5x=-6$$

Divide both sides by 5.

$$x=\frac{-6}{5}$$

Fraction \frac{-6}{5} can be rewritten as -\frac{6}{5} by extracting the negative sign.

$$x=-\frac{6}{5}$$