Intro to Rational Expressions, and Simplifying
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- (Video) Simplifying Rational Expressions by YourMathGal Here's a video by YourMathGal showing you how to simplify rational expressions. She goes through a couple problems showin…
By Alex Federspiel, Liza Sulkin, Amy Feraco, Anusha Rahman
- (Videos) Reducing Rational Expressions by mathman1024 Here's a video by mathman1024 showing you how to reduce rational expressions. Summary\large{\text{Summary}}Summary A ration…
By Alex Federspiel, Liza Sulkin, Amy Feraco, Joshua Siktar, Anusha Rahman
- Rational expressions combine skills from fractions and solving equations A fraction is a number with a top part and a bottom part. The top number is called the numerator, and th…
By Zora Gilbert, Alex Federspiel, Liza Sulkin, Vatsal Ojha, Amy Feraco, Anusha Rahman
- Intro to Rational Expressions and Simplifying A rational expression is a fraction, but instead of just numbers, it has polynomials on the top and bottom. Rational expressions ar…
By Trisha, Anusha Rahman
Problems 34
- Which of the following expressions can you factor and reduce?
- Which of the following expressions equal x2x2−2x\frac{x^2}{x^2-2x}x2−2xx2 when x2−2x≠0x^2-2x\ne0x2−2x=0?
- Which of the following rational expressions do not simplify to polynomials?
- Simplify the following expression. x4−x2−2x2−2\frac{x^4 - x^2 -2}{x^2-2}x2−2x4−x2−2
- Simplify the following expression. x4−2x3+x−2x−2\frac{x^4 - 2x^3+x-2}{x-2}x−2x4−2x3+x−2
- Simplify the following expression: x3+3x2+2xx+1\frac{x^3 + 3x^2 + 2x}{x+1}x+1x3+3x2+2x.
- Simplify 18x527x3\frac{18x^5}{27x^3}27x318x5.
- Simplify 20x4y−15xy4\frac{20x^4y}{-15xy^4}−15xy420x4y.
- Simplify 48x12x3\frac{48x}{12x^3}12x348x.
- Simplify the expression x2+9x+18x+6\frac{x^2+9x+18}{x+6}x+6x2+9x+18.
- Simplify the following expression. x+5x2+25x+100\dfrac{x+5}{x^2+25x+100}x2+25x+100x+5
- Simplify x2+2x−63x2+4x−77\frac{x^2+2x-63}{x^2+4x-77}x2+4x−77x2+2x−63.
- Which of the following equals x2+x−12x2−x−12\frac{x^2+x-12}{x^2-x-12}x2−x−12x2+x−12?
- If x,yx,yx,y are real numbers with product xy=1xy = 1xy=1, find the maximum possible value of the sum 11+x+11+y\frac{1}{1+x} + \frac{1}{1+y}1+x1+1+y1.
- Find the least positive integer n≥14n\ge 14n≥14 for which n−135n+6\frac{n-13}{5n+6}5n+6n−13 is an unsimplified fraction. Source: AHSME 198519851985
- Simplify the expression 3x−6x\frac{3x-6}{x}x3x−6 when x=3x=3x=3.
- Simplify the expression 3x+4yx\frac{3x+4y}{x}x3x+4y when x=4x=4x=4 and y=3y=3y=3.
- Find the value of kkk for which the equation x−1x−3=x−kx−8\frac{x-1}{x-3} = \frac{x-k}{x-8}x−3x−1=x−8x−k has no solutions for xxx.
- Find the average rate of change of g(t)=t2+3t+1g(t)=t^2+3t+1g(t)=t2+3t+1 on the interval [0,a][0,a][0,a]. Your answer will be an expression involving aaa.
- Find the average rate of change of f(x)=x3+2f(x)=x^3+2f(x)=x3+2 on the interval [a,a+h][a,a+h][a,a+h]. Your answer will be an expression involving aaa.
- Simplify the expression x2y4x2\frac{x^{2}y}{4x^{2}}4x2x2y when y=2y = 2y=2 and x≠0x \neq 0x=0.
- Solve for xxx. 6x3+9x2−15xx−1=0\frac{6x^3+9x^2-15x}{x-1}=0x−16x3+9x2−15x=0
- Simplify the rational expression below: x2−1x−1\frac{x^2-1}{x-1}x−1x2−1
- Which of the following is not a solution to this equation: 182x13x=14\frac{182x}{13x}=1413x182x=14
- Simplify the expression. 4x−1−1+x−2x+48−6x−13+13x+7−4x\frac{4x-1-1+x-2x+4}{8-6x-13+13x+7-4x}8−6x−13+13x+7−4x4x−1−1+x−2x+4
- Simplify: 5x+10x+2\frac{5x+10}{x+2}x+25x+10
- Simplify: 6x2+12x3x\frac{6x^{2}+12x}{3x}3x6x2+12x
- Simplify: x2−9x+3\frac{x^{2}-9}{x+3}x+3x2−9
- Simplify: 5x+2510\frac{5x+25}{10}105x+25
- Simplify the following expression: 3xz+4z18x+24\frac{3xz+4z}{18x+24}18x+243xz+4z
- Simplify the following expression: 9xt+t63x+7\frac{9xt+t}{63x+7}63x+79xt+t
- Simplify the following expression: x−3x2−6x+9\frac{x-3}{x^{2}-6x+9}x2−6x+9x−3
- Simplify the following expression: 714x+49\frac{7}{14x+49}14x+497
- 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