Solve {l}{p(1/p)^2+p(1/p)}{+3q-4+3(1/p)}

$$\left. \begin{array} { l } { p ( \frac { 1 } { p } ) ^ { 2 } + p ( \frac { 1 } { p } ) } \\ { + 3 q - 4 + 3 ( \frac { 1 } { p } ) } \end{array} \right.$$

Evaluate

$$3q-3+\frac{4}{p}$$

Short Solution Steps

To raise \frac{1}{p} to a power, raise both numerator and denominator to the power and then divide.

$$p\times \frac{1^{2}}{p^{2}}+p\times \frac{1}{p}+3q-4+3\times \frac{1}{p}$$

Express p\times \frac{1^{2}}{p^{2}} as a single fraction.

$$\frac{p\times 1^{2}}{p^{2}}+p\times \frac{1}{p}+3q-4+3\times \frac{1}{p}$$

Cancel out p in both numerator and denominator.

$$\frac{1^{2}}{p}+p\times \frac{1}{p}+3q-4+3\times \frac{1}{p}$$

Cancel out p and p.

$$\frac{1^{2}}{p}+1+3q-4+3\times \frac{1}{p}$$

Subtract 4 from 1 to get -3.

$$\frac{1^{2}}{p}-3+3q+3\times \frac{1}{p}$$

Express 3\times \frac{1}{p} as a single fraction.

$$\frac{1^{2}}{p}-3+3q+\frac{3}{p}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply -3+3q times \frac{p}{p}.

$$\frac{1^{2}}{p}+\frac{\left(-3+3q\right)p}{p}+\frac{3}{p}$$

Since \frac{1^{2}}{p} and \frac{\left(-3+3q\right)p}{p} have the same denominator, add them by adding their numerators.

$$\frac{1^{2}+\left(-3+3q\right)p}{p}+\frac{3}{p}$$

Do the multiplications in 1^{2}+\left(-3+3q\right)p.

$$\frac{1^{2}-3p+3qp}{p}+\frac{3}{p}$$

Combine like terms in 1^{2}-3p+3qp.

$$\frac{1-3p+3qp}{p}+\frac{3}{p}$$

Since \frac{1-3p+3qp}{p} and \frac{3}{p} have the same denominator, add them by adding their numerators.

$$\frac{1-3p+3qp+3}{p}$$

Combine like terms in 1-3p+3qp+3.

$$\frac{4-3p+3qp}{p}$$

Factor

$$3q-3+\frac{4}{p}$$