Solve 2t/(8-5x)+x=6/x

$$\frac { 2 t } { ( 8 - 5 x ) } + x = \frac { 6 } { x }$$

Solve for t

$$t=-\frac{\left(8-5x\right)\left(x^{2}-6\right)}{2x}$$

$$x\neq \frac{8}{5}\text{ and }x\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by x\left(5x-8\right), the least common multiple of 8-5x,x.

$$-x\times 2t+x\left(5x-8\right)x=\left(5x-8\right)\times 6$$

Multiply -1 and 2 to get -2.

$$-2xt+x\left(5x-8\right)x=\left(5x-8\right)\times 6$$

Multiply x and x to get x^{2}.

$$-2xt+x^{2}\left(5x-8\right)=\left(5x-8\right)\times 6$$

Use the distributive property to multiply x^{2} by 5x-8.

$$-2xt+5x^{3}-8x^{2}=\left(5x-8\right)\times 6$$

Use the distributive property to multiply 5x-8 by 6.

$$-2xt+5x^{3}-8x^{2}=30x-48$$

Subtract 5x^{3} from both sides.

$$-2xt-8x^{2}=30x-48-5x^{3}$$

Add 8x^{2} to both sides.

$$-2xt=30x-48-5x^{3}+8x^{2}$$

The equation is in standard form.

$$\left(-2x\right)t=-5x^{3}+8x^{2}+30x-48$$

Divide both sides by -2x.

$$\frac{\left(-2x\right)t}{-2x}=\frac{\left(8-5x\right)\left(x^{2}-6\right)}{-2x}$$

Dividing by -2x undoes the multiplication by -2x.

$$t=\frac{\left(8-5x\right)\left(x^{2}-6\right)}{-2x}$$

Divide \left(-6+x^{2}\right)\left(8-5x\right) by -2x.

$$t=-\frac{\left(8-5x\right)\left(x^{2}-6\right)}{2x}$$