Solve 4a/a+b*ab+b^2/16aIp_{H}

$$\frac { 4 a } { a + b } \cdot \frac { a b + b ^ { 2 } } { 16 a } Ip _ { H }$$

Evaluate

$$\frac{Ibp_{H}}{4}$$

Short Solution Steps

Multiply \frac{4a}{a+b} times \frac{ab+b^{2}}{16a} by multiplying numerator times numerator and denominator times denominator.

$$\frac{4a\left(ab+b^{2}\right)}{\left(a+b\right)\times 16a}Ip_{H}$$

Cancel out 4a in both numerator and denominator.

$$\frac{ab+b^{2}}{4\left(a+b\right)}Ip_{H}$$

Express \frac{ab+b^{2}}{4\left(a+b\right)}I as a single fraction.

$$\frac{\left(ab+b^{2}\right)I}{4\left(a+b\right)}p_{H}$$

Express \frac{\left(ab+b^{2}\right)I}{4\left(a+b\right)}p_{H} as a single fraction.

$$\frac{\left(ab+b^{2}\right)Ip_{H}}{4\left(a+b\right)}$$

Factor the expressions that are not already factored.

$$\frac{Ibp_{H}\left(a+b\right)}{4\left(a+b\right)}$$

Cancel out a+b in both numerator and denominator.

$$\frac{Ibp_{H}}{4}$$

Expand

$$\frac{Ibp_{H}}{4}$$

Short Solution Steps

Multiply \frac{4a}{a+b} times \frac{ab+b^{2}}{16a} by multiplying numerator times numerator and denominator times denominator.

$$\frac{4a\left(ab+b^{2}\right)}{\left(a+b\right)\times 16a}Ip_{H}$$

Cancel out 4a in both numerator and denominator.

$$\frac{ab+b^{2}}{4\left(a+b\right)}Ip_{H}$$

Express \frac{ab+b^{2}}{4\left(a+b\right)}I as a single fraction.

$$\frac{\left(ab+b^{2}\right)I}{4\left(a+b\right)}p_{H}$$

Express \frac{\left(ab+b^{2}\right)I}{4\left(a+b\right)}p_{H} as a single fraction.

$$\frac{\left(ab+b^{2}\right)Ip_{H}}{4\left(a+b\right)}$$

Factor the expressions that are not already factored.

$$\frac{Ibp_{H}\left(a+b\right)}{4\left(a+b\right)}$$

Cancel out a+b in both numerator and denominator.

$$\frac{Ibp_{H}}{4}$$