Solve 5x/3(x-1)+6/x+2=5/3

$$\frac { 5 x } { 3 ( x - 1 ) } + \frac { 6 } { x + 2 } = \frac { 5 } { 3 }$$

Solve for x

$$x=\frac{8}{23}\approx 0.347826087$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -2,1 since division by zero is not defined. Multiply both sides of the equation by 3\left(x-1\right)\left(x+2\right), the least common multiple of 3\left(x-1\right),x+2,3.

$$\left(x+2\right)\times 5x+\left(3x-3\right)\times 6=5\left(x-1\right)\left(x+2\right)$$

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

$$\left(5x+10\right)x+\left(3x-3\right)\times 6=5\left(x-1\right)\left(x+2\right)$$

Use the distributive property to multiply 5x+10 by x.

$$5x^{2}+10x+\left(3x-3\right)\times 6=5\left(x-1\right)\left(x+2\right)$$

Use the distributive property to multiply 3x-3 by 6.

$$5x^{2}+10x+18x-18=5\left(x-1\right)\left(x+2\right)$$

Combine 10x and 18x to get 28x.

$$5x^{2}+28x-18=5\left(x-1\right)\left(x+2\right)$$

Use the distributive property to multiply 5 by x-1.

$$5x^{2}+28x-18=\left(5x-5\right)\left(x+2\right)$$

Use the distributive property to multiply 5x-5 by x+2 and combine like terms.

$$5x^{2}+28x-18=5x^{2}+5x-10$$

Subtract 5x^{2} from both sides.

$$5x^{2}+28x-18-5x^{2}=5x-10$$

Combine 5x^{2} and -5x^{2} to get 0.

$$28x-18=5x-10$$

Subtract 5x from both sides.

$$28x-18-5x=-10$$

Combine 28x and -5x to get 23x.

$$23x-18=-10$$

Add 18 to both sides.

$$23x=-10+18$$

Add -10 and 18 to get 8.

$$23x=8$$

Divide both sides by 23.

$$x=\frac{8}{23}$$