SAT Math : How to find the solution to a rational equation with LCD

Study concepts, example questions & explanations for SAT Math

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Example Questions

Example Question #172 : Algebra

 Rational_5

Possible Answers:

0

1

–1

2

–2

Correct answer:

2

Explanation:

Rational_2

Rational_3

Rational_4

Example Question #11 : Equations / Inequalities

Linesmb1

Possible Answers:

b/(m+ 1)

bm/(m+ 1)

b/(m– 1)

–bm/(m+ 1)

–b/(+ 1)

Correct answer:

b/(m+ 1)

Explanation:

Linesmb5

Linesmb4

Example Question #106 : Algebra

In the equation below, , , and are non-zero numbers. What is the value of in terms of and ?

Possible Answers:

Correct answer:

Explanation:

Pkm_7-21-13

Pkm2_7-21-13

Example Question #1 : How To Find The Solution To A Rational Equation With Lcd

Solve for x:

Possible Answers:

Correct answer:

Explanation:

The first step is to cancel out the denominator by multiplying both sides by 7:

Subtract 3 from both sides to get  by itself:

Example Question #106 : Linear / Rational / Variable Equations

Solve for  and  using elimination:

Possible Answers:

 and 

 and 

 and 

 and 

 and 

Correct answer:

 and 

Explanation:

When using elimination, you need two factors to cancel out when the two equations are added together. We can get the  in the first equation to cancel out with the  in the second equation by multiplying everything in the second equation by :

Now our two equations look like this:

The  can cancel with the , giving us:

These equations, when summed, give us:

Once we know the value for , we can just plug it into one of our original equations to solve for the value of :

Example Question #2 : How To Find The Solution To A Rational Equation With Lcd

Give the solution set of the rational equation 

Possible Answers:

Correct answer:

Explanation:

Multiply both sides of the equation by the denominator :

Rewrite both expression using the binomial square pattern:

This can be rewritten as a linear equation by subtracting  from both sides:

Solve as a linear equation:

Example Question #3 : How To Find The Solution To A Rational Equation With Lcd

Solve:

Possible Answers:

Correct answer:

Explanation:

Multiply by  on each side

Subtract  on each side

Multiply by  on each side

 

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