Math Calculators, Lessons and Formulas

It is time to solve your math problem

mathportal.org

◀ back to index

Question

Answer

$$2b^3+\dfrac{250}{b^2}+7b+10=\dfrac{2b^5+7b^3+10b^2+250}{b^2}$$

Explanation

Tap the blue circles to see an explanation.

$$ \begin{aligned}2b^3+\frac{250}{b^2}+7b+10& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{2b^5+250}{b^2}+7b+10 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{2b^5+7b^3+250}{b^2}+10 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{2b^5+7b^3+10b^2+250}{b^2}\end{aligned} $$
①

Add $2b^3$ and $ \dfrac{250}{b^2} $ to get $ \dfrac{ \color{purple}{ 2b^5+250 } }{ b^2 }$.

Step 1: Write $ 2b^3 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator.

Step 2: To add raitonal expressions, both fractions must have the same denominator.
We can create a common denominator by multiplying the first fraction by $\color{blue}{ b^2 }$.

$$ \begin{aligned} 2b^3+ \frac{250}{b^2} & \xlongequal{\text{Step 1}} \frac{2b^3}{\color{red}{1}} + \frac{250}{b^2} = \frac{ 2b^3 \cdot \color{blue}{ b^2 }}{ 1 \cdot \color{blue}{ b^2 }} + \frac{ 250 }{ b^2 } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 2b^5 } }{ b^2 } + \frac{ \color{purple}{ 250 } }{ b^2 }=\frac{ \color{purple}{ 2b^5+250 } }{ b^2 } \end{aligned} $$
②

Add $ \dfrac{2b^5+250}{b^2} $ and $ 7b $ to get $ \dfrac{ \color{purple}{ 2b^5+7b^3+250 } }{ b^2 }$.

Step 1: Write $ 7b $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator.

Step 2: To add raitonal expressions, both fractions must have the same denominator.
We can create a common denominator by multiplying the second fraction by $\color{blue}{b^2}$.

$$ \begin{aligned} \frac{2b^5+250}{b^2} +7b & \xlongequal{\text{Step 1}} \frac{2b^5+250}{b^2} + \frac{7b}{\color{red}{1}} = \frac{ 2b^5+250 }{ b^2 } + \frac{ 7b \cdot \color{blue}{ b^2 }}{ 1 \cdot \color{blue}{ b^2 }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 2b^5+250 } }{ b^2 } + \frac{ \color{purple}{ 7b^3 } }{ b^2 }=\frac{ \color{purple}{ 2b^5+7b^3+250 } }{ b^2 } \end{aligned} $$
③

Add $ \dfrac{2b^5+7b^3+250}{b^2} $ and $ 10 $ to get $ \dfrac{ \color{purple}{ 2b^5+7b^3+10b^2+250 } }{ b^2 }$.

Step 1: Write $ 10 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator.

Step 2: To add raitonal expressions, both fractions must have the same denominator.
We can create a common denominator by multiplying the second fraction by $\color{blue}{b^2}$.

$$ \begin{aligned} \frac{2b^5+7b^3+250}{b^2} +10 & \xlongequal{\text{Step 1}} \frac{2b^5+7b^3+250}{b^2} + \frac{10}{\color{red}{1}} = \frac{ 2b^5+7b^3+250 }{ b^2 } + \frac{ 10 \cdot \color{blue}{ b^2 }}{ 1 \cdot \color{blue}{ b^2 }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 2b^5+7b^3+250 } }{ b^2 } + \frac{ \color{purple}{ 10b^2 } }{ b^2 }=\frac{ \color{purple}{ 2b^5+7b^3+10b^2+250 } }{ b^2 } \end{aligned} $$
This page was created using
Simplify Rational Expressions