Math Calculators, Lessons and Formulas

It is time to solve your math problem

mathportal.org

back to index

Answer

$$\frac{7x+3}{3-x}+\frac{5}{x-3}=\frac{7x-2}{-x+3}$$

Explanation

$$ \begin{aligned}\frac{7x+3}{3-x}+\frac{5}{x-3}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{7x-2}{-x+3}\end{aligned} $$
①

Add $ \dfrac{7x+3}{3-x} $ and $ \dfrac{5}{x-3} $ to get $ \dfrac{ \color{purple}{ 7x-2 } }{ -x+3 }$.

To add raitonal expressions, both fractions must have the same denominator.
We can create a common denominator by multiplying the second fraction by $\color{blue}{-1}$.

$$ \begin{aligned} \frac{7x+3}{3-x} + \frac{5}{x-3} & = \frac{ 7x+3 }{ 3-x } + \frac{ 5 \cdot \color{blue}{ \left( -1 \right) }}{ \left( x-3 \right) \cdot \color{blue}{ \left( -1 \right) }} = \\[1ex] &=\frac{ \color{purple}{ 7x+3 } }{ 3-x } + \frac{ \color{purple}{ -5 } }{ 3-x }=\frac{ \color{purple}{ 7x-2 } }{ -x+3 } \end{aligned} $$
This page was created using
Simplify Rational Expressions