Practice Problems

Solve each Rational Inequality

\(\textbf{1)}\) \(\displaystyle \frac{{6-x}}{{x+5}}\gt0\)

Show Answer

\(-5 \lt x \lt 6 \)
\((-5,6)\)

 

\(\textbf{2)}\) \(\displaystyle \frac{{3x-5}}{{x-3}} \le 0\)

Show Answer

\( \frac{5}{3} \le x \lt 3 \)
\(\left(\frac{5}{3},3\right)\)

 

\(\textbf{3)}\) \(\displaystyle \frac{{{x^2}+3x+2}}{{x+1}} \ge 0\)

Show Answer

\(-2 \le x \lt -1 \text{ or } x \gt -1\)
\((-2,-1)\cup(-1,\infty) \)

 

\(\textbf{4)}\) \(\displaystyle \frac{{5x+3}}{{x+2}} \lt – 1\)

Show Answer

\(-2 \lt x \lt -\frac{5}{6}\)
\(\left(-2,-\frac{5}{6}\right)\)

 

\(5)\) \(\displaystyle \frac{{{x^3}-2{x^2}}}{{x+2}} \gt 0\)

Show Answer

\(x \lt -2 \text{ or } x \gt 2\)
\((-\infty,-2)\cup(2,\infty) \)

 

 

See Related Pages\(\)

\(\bullet\text{ Rational Inequality Calculator }\)
\(\,\,\,\,\,\,\,\,\text{(Symbolab.com)}\)

\(\bullet\text{ Algebra 2/ Precalculus Homepage}\)
\(\,\,\,\,\,\,\,\,\text{All the Best Topics…}\)

\(\bullet\text{ Polynomial Inequalities}\)
\(\,\,\,\,\,\,\,\,x^3-4x^2-4x+16 \gt 0…\)

\(\bullet\text{ Rational Expressions- Multiplying and Dividing}\)
\(\,\,\,\,\,\,\,\,\displaystyle\frac{x^2+3x-4}{(x+4)(x+5)}\cdot \displaystyle\frac{x+5}{x-1}…\)

\(\bullet\text{ Rational Expressions- Adding and Subtracting}\)
\(\,\,\,\,\,\,\,\,\displaystyle\frac{x-5}{x+3}+\frac{x+2}{x^2+5x+6}…\)

\(\bullet\text{ Complex Fractions}\)
\(\,\,\,\,\,\,\,\,\displaystyle\frac{\frac{x}{5}+\frac{1}{3}}{\frac{1}{5}-\frac{1}{6}}…\)

\(\bullet\text{ Partial Fraction Decomposition}\)
\(\,\,\,\,\,\,\,\,\displaystyle\frac{8x+10}{x^2+2x}=\displaystyle\frac{5}{x} + \frac{3}{x+2}…\)