Intro to Dividing Rational Expressions
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- (Video) Divide Rational Expressions by mathman1024 Here's a video by mathman1024 showing you how to divide two rational expressions. Dividing rational expressions is a lot like …
By Alex Federspiel, Amy Feraco, Anusha Rahman
- Examples: Dividing rational expressions \\ Diving a fraction is equivalent to multiplying its reciprocal. Recall how we divide a fraction: Once the division becomes multiplicati…
By Christine, Victor Wang, Joshua Siktar, Anusha Rahman
- Expressions with Rational Numbers A rational number is a number that can be expressed in the form ab\frac{a}{b}ba where aaa and bbb are integers and b≠0b \ne 0b=0. These are n…
By Eunji Kwon, Jonathan Heller, Alex Federspiel, Anusha Rahman
- Intro to Dividing Rational Expressions A rational expression is a fraction where the numerator and/or the denominator are polynomials. When we divide rational expressions, we fo…
By Trisha, Anusha Rahman
Problems 34
- Simplify 10x2+9x−8x2\frac{10x^2 + 9x -8}{x^2}x210x2+9x−8 when x≠0x\ne0x=0.
- If U=x2−1U = x^2 -1U=x2−1 and V=x2+2x+1V = x^2 + 2x+1V=x2+2x+1, what is UUU divided by VVV? (Hint: It is a good idea to factor UUU and/or VVV before you divide.)
- Simplify x2−x−2x2+x−6 ÷x2+6x+8x2+7x+12\frac{x^2-x-2}{x^2+x-6}\ \div\frac{x^2+6x+8}{x^2+7x+12}x2+x−6x2−x−2 ÷x2+7x+12x2+6x+8 when x>10x>10x>10.
- Simplify x2−8x+7x2−12x+35x2+6x−27x2−8x+15\dfrac{\dfrac{x^2-8x+7}{x^2-12x+35}}{\dfrac{x^2+6x-27}{x^2-8x+15}}x2−8x+15x2+6x−27x2−12x+35x2−8x+7 when x>10x>10x>10.
- Simplify x8−4x÷x26−3x\frac{x}{8-4x}\div\frac{x^2}{6-3x}8−4xx÷6−3xx2 when x>10x>10x>10.
- Simplify x2−4x+4x2+5x−14÷3x2−17x−6x2+x−42\frac{x^2-4x+4}{x^2+5x-14}\div\frac{3x^2-17x-6}{x^2+x-42}x2+5x−14x2−4x+4÷x2+x−423x2−17x−6 when xxx is not an integer.
- Simplify x2−xx2+x−2 ÷1+1xx2+3x+2\frac{x^2-x}{x^2+x-2}\ \div\frac{1+\frac{1}{x}}{x^2+3x+2}x2+x−2x2−x ÷x2+3x+21+x1 when xxx is not an integer.
- Simplify x2−17x+70x2−14x+40 ÷x2−2x−35x2+x−20\frac{x^2-17x+70}{x^2-14x+40}\ \div\frac{x^2-2x-35}{x^2+x-20}x2−14x+40x2−17x+70 ÷x2+x−20x2−2x−35 when xxx is not an integer.
- Simplify 3x2+11x−70x2+x−42 ÷−3x2+31x−70x2−13x+42\frac{3x^2+11x-70}{x^2+x-42}\ \div\frac{-3x^2+31x-70}{x^2-13x+42}x2+x−423x2+11x−70 ÷x2−13x+42−3x2+31x−70 when x>10x > 10x>10.
- Simplify 6x5÷65x\frac{6x}{5}\div\frac{6}{5x}56x÷5x6 if x≠0x\neq0x=0.
- Simplify 7(x+3)21÷3x+97x.\frac{7(x+3)}{21} \div\frac{3x+9}{7x}.217(x+3)÷7x3x+9.
- Evaluate x2−5x+6x2−3x+2÷x2−7x+12x2−5x+4\frac{x^2-5x+6}{x^2-3x+2} \div \frac{x^2-7x+12}{x^2-5x+4}x2−3x+2x2−5x+6÷x2−5x+4x2−7x+12 when x=2017x = 2017x=2017.
- Simplify ∣x+y∣∣−x−y∣\frac{|x+y|}{|-x-y|}∣−x−y∣∣x+y∣ where x≠−y.x \neq -y.x=−y.
- Simplify ∣x2−1∣∣1−x∣\frac{|x^2-1|}{|1-x|}∣1−x∣∣x2−1∣ if x≠1x \neq 1x=1
- Evaluate ∣x+2∣∣x∣∣y−1∣∣1−y∣\frac{|x+2||x||y-1|}{|1-y|}∣1−y∣∣x+2∣∣x∣∣y−1∣ if x=−1x=-1x=−1 and y≠1.y \neq 1.y=1.
- Simplify ∣(−x)(−y)(z)∣∣(x)(y)(−z)∣\frac{|(-x)(-y)(z)|}{|(x)(y)(-z)|}∣(x)(y)(−z)∣∣(−x)(−y)(z)∣ if x,y,zx, y, zx,y,z are nonzero.
- Simplify the following expression. 3x4+6x33x÷x2\frac{3x^4+6x^3}{3x}\div x^23x3x4+6x3÷x2 (Assume x≠0x\neq0x=0.)
- Simplify 9x+4÷3x+4\frac{9}{x+4}\div\frac{3}{x+4}x+49÷x+43 if x≠−4x\neq-4x=−4.
- Simplify x2−1x+1÷xx−1\frac{x^2-1}{x+1}\div \frac{x}{x-1}x+1x2−1÷x−1x if x≠−1,0,1x\neq-1,0,1x=−1,0,1.
- Simplify (x−1)2x2÷(x−1)(x2+1)\frac{\sqrt{(x-1)^2}}{x^2}\div\frac{(x-1)}{(x^2+1)}x2(x−1)2÷(x2+1)(x−1) assuming that x>1x > 1x>1.
- Simplify x2−x3x÷x(x+1)9x2−9\frac{x^2-x}{3\sqrt{x}}\div \frac{\sqrt{x}(x+1)}{9x^2-9}3xx2−x÷9x2−9x(x+1) assuming x>1x>1x>1.
- Which of the following is equivalent to x2+3x+2x÷33x2−3x−18\frac{x^2+3x+2}{x}\div\frac{3}{3x^2-3x-18}xx2+3x+2÷3x2−3x−183 assuming xxx and 3x2−3x−183x^2-3x-183x2−3x−18 are nonz…
- Simplify x2−5x+6x2−4÷x2+9−6xx2.\frac{x^2-5x+6}{x^2-4}\div \frac{x^2+9-6x}{x^2}.x2−4x2−5x+6÷x2x2+9−6x.
- Simplify x4x3÷5xx−1.\frac{x}{4x^3}\div\frac{5x}{x^{-1}}.4x3x÷x−15x.
- Simplify the expression. 9x4⋅3−y8÷32⋅11−13y\frac{9x}{4}\cdot\frac{3-y}{8}\div\frac{3}{2}\cdot\frac{1}{1-\frac13y}49x⋅83−y÷23⋅1−31y1
- Simplify: x33x−1÷x24x+9\frac{x^{3}}{3x-1} \div \frac{x^{2}}{4x+9}3x−1x3÷4x+9x2
- Simplify the following expression: 6x+12÷9x+24\frac{6x+1}{2} \div \frac{9x+2}{4}26x+1÷49x+2
- Simplify the following expression: x2+2x+13÷x2−16\frac{x^{2}+2x+1}{3} \div \frac{x^{2}-1}{6}3x2+2x+1÷6x2−1
- Simplify the following expression if t≠1t \neq 1t=1 and t≠−1t \neq -1t=−1: t2+1t+1÷t2−1t−1\frac{t^{2}+1}{t+1} \div \frac{t^{2}-1}{t-1}t+1t2+1÷t−1t2−1
- Simplify the following expression when t≠1t \neq 1t=1 and t≠−1:t \neq -1:t=−1: t2−1t−1÷t+1t−1\frac{t^{2}-1}{t-1} \div \frac{t+1}{t-1}t−1t2−1÷t−1t+1
- Simplify the following expression: −x−318÷x+39\frac{-x-3}{18} \div \frac{x+3}{9}18−x−3÷9x+3
- Simplify the following expression: 414−7x÷821−14x\frac{4}{14-7x} \div \frac{8}{21-14x}14−7x4÷21−14x8
- Simplify the following expression: 9x4x+2÷38x+4\frac{9x}{4x+2} \div \frac{3}{8x+4}4x+29x÷8x+43
- Solve the equation for positive xxx: x2+3x4x+6=x+36\frac{x^2 + 3x}{4x + 6} = \frac{x + 3}{6}4x+6x2+3x=6x+3