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

Study concepts, example questions & explanations for ACT Math

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Example Questions

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

John, Jill, and Jack are splitting a pizza. John eats  of the pizza and Jill eats  of the pizza. How much of the pizza is left for Jack?

Possible Answers:

Correct answer:

Explanation:

We can write an equation for the amount of pizza eaten, with  as the amount left for Jack.

To solve this equation, we must find the lowest common denominator of  and . We can list the multiples of  and  to find the least common multiple:

We can see that the least common multiple of  and  is , so we can rewrite each of the fractions with a denominator of .

When we put these fractions back into the equation, we can solve for :

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

What is the slope of a line represented by the equation:

Possible Answers:

Correct answer:

Explanation:

To solve problems where you need to find the slope of a line in a given equation, change the equation so that it matches y-intercept form:

For this equation, first move the 3x over to the other side of the equation.

            

The equation should now look like this:

Then, divide by 15 to isolate the variable .

Then simplify

Whatever number is before the x in the equation (m) is your slope.

Example Question #54 : Algebra

 Rational_5

Possible Answers:

2

–1

1

–2

0

Correct answer:

2

Explanation:

Rational_2

Rational_3

Rational_4

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

Linesmb1

Possible Answers:

bm/(m+ 1)

b/(m+ 1)

–b/(+ 1)

b/(m– 1)

–bm/(m+ 1)

Correct answer:

b/(m+ 1)

Explanation:

Linesmb5

Linesmb4

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

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

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