Algebra
Topics

# How do you write the mixed expression n^2+(n-1)/(n+4) as a rational expression?

##### 1 Answer
May 2, 2017

$\frac{{n}^{3} + 4 {n}^{2} + n - 1}{n + 4}$

#### Explanation:

A rational expression is an algebraic fraction with a $\textcolor{b l u e}{\text{polynomial}}$ on the numerator and denominator.

$\text{before adding the mixed expression we require the terms}$

$\text{to have a "color(blue)"common denominator}$

$\text{multiply " n^2" by } \frac{n + 4}{n + 4}$

$\Rightarrow \frac{{n}^{2} \left(n + 4\right)}{n + 4} + \frac{n - 1}{n + 4}$

Now the 2 terms have a common denominator we can add the numerators leaving the denominator as it is.

$\Rightarrow \frac{{n}^{3} + 4 {n}^{2} + n - 1}{n + 4} \leftarrow \textcolor{red}{\text{ rational expression}}$

##### Impact of this question
487 views around the world
You can reuse this answer
Creative Commons License
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 7, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9880943894386292, "perplexity": 2804.1076086746157}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-49/segments/1637964359037.96/warc/CC-MAIN-20211130141247-20211130171247-00214.warc.gz"}