Math Calculators, Lessons and Formulas

It is time to solve your math problem

mathportal.org

◀ back to index

Question

Answer

$$x^2+\dfrac{3}{2}x^4-2-(2+\dfrac{3}{2}x^4)=\dfrac{2x^2-8}{2}$$

Explanation

Tap the blue circles to see an explanation.

$$ \begin{aligned}x^2+\frac{3}{2}x^4-2-(2+\frac{3}{2}x^4)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}x^2+\frac{3x^4}{2}-2-(2+\frac{3x^4}{2}) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}\frac{3x^4+2x^2}{2}-2-\frac{3x^4+4}{2} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} \htmlClass{explanationCircle explanationCircle6}{\textcircled {6}} } }}}\frac{3x^4+2x^2-4}{2}-\frac{3x^4+4}{2} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle7}{\textcircled {7}} } }}}\frac{2x^2-8}{2}\end{aligned} $$
①

Multiply $ \dfrac{3}{2} $ by $ x^4 $ to get $ \dfrac{ 3x^4 }{ 2 } $.

Step 1: Write $ x^4 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} \frac{3}{2} \cdot x^4 & \xlongequal{\text{Step 1}} \frac{3}{2} \cdot \frac{x^4}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 3 \cdot x^4 }{ 2 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 3x^4 }{ 2 } \end{aligned} $$
②

Multiply $ \dfrac{3}{2} $ by $ x^4 $ to get $ \dfrac{ 3x^4 }{ 2 } $.

Step 1: Write $ x^4 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} \frac{3}{2} \cdot x^4 & \xlongequal{\text{Step 1}} \frac{3}{2} \cdot \frac{x^4}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 3 \cdot x^4 }{ 2 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 3x^4 }{ 2 } \end{aligned} $$
③

Add $x^2$ and $ \dfrac{3x^4}{2} $ to get $ \dfrac{ \color{purple}{ 3x^4+2x^2 } }{ 2 }$.

Step 1: Write $ x^2 $ 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 $\color{blue}{ 2 }$.

$$ \begin{aligned} x^2+ \frac{3x^4}{2} & \xlongequal{\text{Step 1}} \frac{x^2}{\color{red}{1}} + \frac{3x^4}{2} = \frac{ x^2 \cdot \color{blue}{ 2 }}{ 1 \cdot \color{blue}{ 2 }} + \frac{ 3x^4 }{ 2 } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 2x^2 } }{ 2 } + \frac{ \color{purple}{ 3x^4 } }{ 2 }=\frac{ \color{purple}{ 3x^4+2x^2 } }{ 2 } \end{aligned} $$
④

Add $2$ and $ \dfrac{3x^4}{2} $ to get $ \dfrac{ \color{purple}{ 3x^4+4 } }{ 2 }$.

Step 1: Write $ 2 $ 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 $\color{blue}{ 2 }$.

$$ \begin{aligned} 2+ \frac{3x^4}{2} & \xlongequal{\text{Step 1}} \frac{2}{\color{red}{1}} + \frac{3x^4}{2} = \frac{ 2 \cdot \color{blue}{ 2 }}{ 1 \cdot \color{blue}{ 2 }} + \frac{ 3x^4 }{ 2 } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 4 } }{ 2 } + \frac{ \color{purple}{ 3x^4 } }{ 2 }=\frac{ \color{purple}{ 3x^4+4 } }{ 2 } \end{aligned} $$
⑤

Subtract $2$ from $ \dfrac{3x^4+2x^2}{2} $ to get $ \dfrac{ \color{purple}{ 3x^4+2x^2-4 } }{ 2 }$.

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

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

$$ \begin{aligned} \frac{3x^4+2x^2}{2} -2 & \xlongequal{\text{Step 1}} \frac{3x^4+2x^2}{2} - \frac{2}{\color{red}{1}} = \frac{ 3x^4+2x^2 }{ 2 } - \frac{ 2 \cdot \color{blue}{ 2 }}{ 1 \cdot \color{blue}{ 2 }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 3x^4+2x^2 } }{ 2 } - \frac{ \color{purple}{ 4 } }{ 2 }=\frac{ \color{purple}{ 3x^4+2x^2-4 } }{ 2 } \end{aligned} $$
⑥

Add $2$ and $ \dfrac{3x^4}{2} $ to get $ \dfrac{ \color{purple}{ 3x^4+4 } }{ 2 }$.

Step 1: Write $ 2 $ 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 $\color{blue}{ 2 }$.

$$ \begin{aligned} 2+ \frac{3x^4}{2} & \xlongequal{\text{Step 1}} \frac{2}{\color{red}{1}} + \frac{3x^4}{2} = \frac{ 2 \cdot \color{blue}{ 2 }}{ 1 \cdot \color{blue}{ 2 }} + \frac{ 3x^4 }{ 2 } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 4 } }{ 2 } + \frac{ \color{purple}{ 3x^4 } }{ 2 }=\frac{ \color{purple}{ 3x^4+4 } }{ 2 } \end{aligned} $$
⑦

Subtract $ \dfrac{3x^4+4}{2} $ from $ \dfrac{3x^4+2x^2-4}{2} $ to get $ \dfrac{2x^2-8}{2} $.

To subtract expressions with the same denominators, we subtract the numerators and write the result over the common denominator.

$$ \begin{aligned} \frac{3x^4+2x^2-4}{2} - \frac{3x^4+4}{2} & = \frac{3x^4+2x^2-4}{\color{blue}{2}} - \frac{3x^4+4}{\color{blue}{2}} = \\[1ex] &=\frac{ 3x^4+2x^2-4 - \left( 3x^4+4 \right) }{ \color{blue}{ 2 }}= \frac{2x^2-8}{2} \end{aligned} $$
This page was created using
Simplify polynomials calculator