Solving Rational Equations, in Depth
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- (Videos) Solving Rational Equations by mathman1024 Here's a video by mathman1024 where he shows you how to solve rational equations. Rational equations are equations that contai…
By Alex Federspiel, Anusha Rahman
- (Videos) Solving with Multiple Rational Expressions by mathman1024 Here's a video by mathman1024 showing you how to solve rational equations. In this example there's multiple ra…
By Alex Federspiel, Anusha Rahman
- Background In the previous lessons, we learned how to simplify rational expressions, whether they're added/subtracted or multiplied/divided together. We can extend these concept…
By Anusha Rahman
- Solving Rational Equations In this lesson, we will learn how to solve rational equations. A rational equation is similar to a rational expression, but now there is an equal sign…
By Anusha Rahman
Problems 14
- Solve 4+x4−x=2+x2−x\frac{4+x}{4-x}=\frac{2+x}{2-x}4−x4+x=2−x2+x
- Solve for xxx. 4xx+6x=8\frac{4x}{x}+\frac{6}{x}=8x4x+x6=8
- Solve for xxx. 1x =116x −8\frac{1}{x}\ =\frac{11}{6x}\ -8x1 =6x11 −8
- Solve for xxx. 1x +11x+6x2−2x =2x+3x2−2x\frac{1}{x}\ +\frac{11x+6}{x^2-2x}\ =\frac{2x+3}{x^2-2x}x1 +x2−2x11x+6 =x2−2x2x+3
- List all solutions of the equation 18x2−9−3x−3=1.\frac{18}{x^2-9} - \frac{3}{x-3} = 1.x2−918−x−33=1.
- Find the largest solution to the equation 11−x+11+x+1=0.\frac{1}{1-x} + \frac{1}{1+x} + 1 = 0.1−x1+1+x1+1=0.
- How many solutions to the equation 11+x+11−x=0\frac{1}{1+x} + \frac{1}{1-x} = 01+x1+1−x1=0 are there?
- Solve the rational equation 1a−3+1a−5=0\frac1{a-3} + \frac1{a-5} = 0a−31+a−51=0.
- Find the smallest solution to 2(x−1)2=18\frac{2}{(x-1)^2} = 18(x−1)22=18.
- Let f(x)=1xf(x) = \frac{1}{x}f(x)=x1. If ccc is a real number satisfying f(c)=4cf(c) = 4cf(c)=4c, then what is f(c5)f(\frac{c}{5})f(5c)?
- Find the point of intersection for y=3x−8y=\frac3{x-8}y=x−83 and y=3y=3y=3.
- A Pittsburgh river tour lasts 222 hours. The boat goes 101010 km upstream and then back. The river's current is measured as 1.51.51.5 km per hour. What is the boat's speed?
- Solve equation (A) and plug the result into expression (B). xx−6=2(A)6x2−x(B)\begin{array}{lc} \frac{x}{x-6}=2&\quad\small{(A)}\\ \frac{6}{x^2-x}&\quad\small{(B)} \end{array}x−6…
- Solve for xxx. 6x3+9x2−15xx−1=0\frac{6x^3+9x^2-15x}{x-1}=0x−16x3+9x2−15x=0