Solve 7+2/7-frac{2{1+x}}=1

$$7 + \frac { 2 } { 7 - \frac { 2 } { 1 + x } } = 1$$

Solve for x

$$x=-\frac{8}{11}\approx -0.727272727$$

Steps for Solving Linear Equation

To add or subtract expressions, expand them to make their denominators the same. Multiply 7 times \frac{1+x}{1+x}.

$$7+\frac{2}{\frac{7\left(1+x\right)}{1+x}-\frac{2}{1+x}}=1$$

Since \frac{7\left(1+x\right)}{1+x} and \frac{2}{1+x} have the same denominator, subtract them by subtracting their numerators.

$$7+\frac{2}{\frac{7\left(1+x\right)-2}{1+x}}=1$$

Do the multiplications in 7\left(1+x\right)-2.

$$7+\frac{2}{\frac{7+7x-2}{1+x}}=1$$

Combine like terms in 7+7x-2.

$$7+\frac{2}{\frac{5+7x}{1+x}}=1$$

Variable x cannot be equal to -1 since division by zero is not defined. Divide 2 by \frac{5+7x}{1+x} by multiplying 2 by the reciprocal of \frac{5+7x}{1+x}.

$$7+\frac{2\left(1+x\right)}{5+7x}=1$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 7 times \frac{5+7x}{5+7x}.

$$\frac{7\left(5+7x\right)}{5+7x}+\frac{2\left(1+x\right)}{5+7x}=1$$

Since \frac{7\left(5+7x\right)}{5+7x} and \frac{2\left(1+x\right)}{5+7x} have the same denominator, add them by adding their numerators.

$$\frac{7\left(5+7x\right)+2\left(1+x\right)}{5+7x}=1$$

Do the multiplications in 7\left(5+7x\right)+2\left(1+x\right).

$$\frac{35+49x+2+2x}{5+7x}=1$$

Combine like terms in 35+49x+2+2x.

$$\frac{37+51x}{5+7x}=1$$

Variable x cannot be equal to -\frac{5}{7} since division by zero is not defined. Multiply both sides of the equation by 7x+5.

$$37+51x=7x+5$$

Subtract 7x from both sides.

$$37+51x-7x=5$$

Combine 51x and -7x to get 44x.

$$37+44x=5$$

Subtract 37 from both sides.

$$44x=5-37$$

Subtract 37 from 5 to get -32.

$$44x=-32$$

Divide both sides by 44.

$$x=\frac{-32}{44}$$

Reduce the fraction \frac{-32}{44} to lowest terms by extracting and canceling out 4.

$$x=-\frac{8}{11}$$