A scale model of a racecar is in the ratio of 1:x to the real racecar. The length of the model is
Guidance
A rational equation is an equation where there are rational expressions on both sides of the equal sign. One way to solve rational equations is to use crossmultiplication. Here is an example of a proportion that we can solve using crossmultiplication.
If you need more of a review of crossmultiplication, see the Proportion Properties concept. Otherwise, we will start solving rational equations using crossmultiplication.
Example A
Solve
Solution: Use crossmultiplication to solve the problem. You can use the example above as a guideline.
Check your answers. It is possible to get extraneous solutions with rational expressions.
Example B
Solve
Solution: Crossmultiply and solve.
Check your answers.
Example C
Solve
Solution: Crossmultiply.
Check the answer:
Intro Problem Revisit We need to set up a rational equation and solve for x.
Now crossmultiply.
However, x is a ratio so it must be greater than 0. Therefore x equals 21 and the model is in the ratio 1:21 to the real racecar.
Guided Practice
Solve the following rational equations.
1.
2.
3.
Answers
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2.
3.
Problem Set
 Is
x=−2 a solution tox−1x−4=x2−1x+4 ?
Solve the following rational equations.

2xx+3=8x 
4x+1=x+23 
x2x+2=x+32 
3x2x−1=2x+1x 
x+2x−3=x3x−2 
x+3−3=2x+6x−3 
2x+5x−1=2x−4 
6x−14x2=32x+5 
5x2+110=x3−82x 
x2−4x+4=2x−13
Determine the values of a that make each statement true. If there no values, write none.

1x−a=xx+a , such that there is no solution. 
1x−a=xx−a , such that there is no solution. 
x−ax=1x+a , such that there is one solution. 
1x+a=xx−a , such that there are two integer solutions.