Solve p-2/5/p+frac{2{5}}=5

$$\frac { p - \frac { 2 } { 5 } } { p + \frac { 2 } { 5 } } = 5$$

Solve for p

$$p=-\frac{3}{5}=-0.6$$

Steps for Solving Linear Equation

Factor the expressions that are not already factored in \frac{p-\frac{2}{5}}{p+\frac{2}{5}}.

$$\frac{\frac{1}{5}\left(5p-2\right)}{\frac{1}{5}\left(5p+2\right)}=5$$

To divide powers of the same base, subtract the numerator's exponent from the denominator's exponent.

$$\frac{5p-2}{\left(\frac{1}{5}\right)^{0}\left(5p+2\right)}=5$$

Calculate \frac{1}{5} to the power of 0 and get 1.

$$\frac{5p-2}{1\left(5p+2\right)}=5$$

Use the distributive property to multiply 1 by 5p+2.

$$\frac{5p-2}{5p+2}=5$$

Variable p cannot be equal to -\frac{2}{5} since division by zero is not defined. Multiply both sides of the equation by 5p+2.

$$5p-2=5\left(5p+2\right)$$

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

$$5p-2=25p+10$$

Subtract 25p from both sides.

$$5p-2-25p=10$$

Combine 5p and -25p to get -20p.

$$-20p-2=10$$

Add 2 to both sides.

$$-20p=10+2$$

Add 10 and 2 to get 12.

$$-20p=12$$

Divide both sides by -20.

$$p=\frac{12}{-20}$$

Reduce the fraction \frac{12}{-20} to lowest terms by extracting and canceling out 4.

$$p=-\frac{3}{5}$$