Solve 7x/7x+8-7/x+6=1

$$\frac { 7 x } { 7 x + 8 } - \frac { 7 } { x + 6 } = 1$$

Solve for x

$$x = -\frac{104}{57} = -1\frac{47}{57} \approx -1.824561404$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -6,-\frac{8}{7} since division by zero is not defined. Multiply both sides of the equation by \left(x+6\right)\left(7x+8\right), the least common multiple of 7x+8,x+6.

$$\left(x+6\right)\times 7x-\left(7x+8\right)\times 7=\left(x+6\right)\left(7x+8\right)$$

Use the distributive property to multiply x+6 by 7.

$$\left(7x+42\right)x-\left(7x+8\right)\times 7=\left(x+6\right)\left(7x+8\right)$$

Use the distributive property to multiply 7x+42 by x.

$$7x^{2}+42x-\left(7x+8\right)\times 7=\left(x+6\right)\left(7x+8\right)$$

Use the distributive property to multiply 7x+8 by 7.

$$7x^{2}+42x-\left(49x+56\right)=\left(x+6\right)\left(7x+8\right)$$

To find the opposite of 49x+56, find the opposite of each term.

$$7x^{2}+42x-49x-56=\left(x+6\right)\left(7x+8\right)$$

Combine 42x and -49x to get -7x.

$$7x^{2}-7x-56=\left(x+6\right)\left(7x+8\right)$$

Use the distributive property to multiply x+6 by 7x+8 and combine like terms.

$$7x^{2}-7x-56=7x^{2}+50x+48$$

Subtract 7x^{2} from both sides.

$$7x^{2}-7x-56-7x^{2}=50x+48$$

Combine 7x^{2} and -7x^{2} to get 0.

$$-7x-56=50x+48$$

Subtract 50x from both sides.

$$-7x-56-50x=48$$

Combine -7x and -50x to get -57x.

$$-57x-56=48$$

Add 56 to both sides.

$$-57x=48+56$$

Add 48 and 56 to get 104.

$$-57x=104$$

Divide both sides by -57.

$$x=\frac{104}{-57}$$

Fraction \frac{104}{-57} can be rewritten as -\frac{104}{57} by extracting the negative sign.

$$x=-\frac{104}{57}$$