Solve 7/3x+4/6x^2=5/8x-2/3x^2

$$\frac { 7 } { 3 x } + \frac { 4 } { 6 x ^ { 2 } } = \frac { 5 } { 8 x } - \frac { 2 } { 3 x ^ { 2 } }$$

Solve for x

$$x=-\frac{32}{41}\approx -0.780487805$$

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 24x^{2}, the least common multiple of 3x,6x^{2},8x,3x^{2}.

$$8x\times 7+4\times 4=3x\times 5-8\times 2$$

Multiply 8 and 7 to get 56.

$$56x+4\times 4=3x\times 5-8\times 2$$

Multiply 4 and 4 to get 16.

$$56x+16=3x\times 5-8\times 2$$

Multiply 3 and 5 to get 15.

$$56x+16=15x-8\times 2$$

Multiply -8 and 2 to get -16.

$$56x+16=15x-16$$

Subtract 15x from both sides.

$$56x+16-15x=-16$$

Combine 56x and -15x to get 41x.

$$41x+16=-16$$

Subtract 16 from both sides.

$$41x=-16-16$$

Subtract 16 from -16 to get -32.

$$41x=-32$$

Divide both sides by 41.

$$x=\frac{-32}{41}$$

Fraction \frac{-32}{41} can be rewritten as -\frac{32}{41} by extracting the negative sign.

$$x=-\frac{32}{41}$$