How to find the solution to a rational equation with LCD

Help Questions

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

Questions 1 - 5

1

Linesmb1

bm/(_m_2 + 1)

–bm/(_m_2 + 1)

–b/(m + 1)

–b/(_m_2 – 1)

b/(_m_2 + 1)

Explanation

Linesmb5

Linesmb4

2

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

$-\frac{1}{5}$

$\frac{4}{3}$

$\frac{1}{5}$

$\frac{3}{4}$

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 .

$\frac{15y}{15} =-\frac{3x}{15} + \frac{4}{15} \rightarrow y =-\frac{3}{15}x + \frac{4}{15}$

Then simplify

$y =-\frac{3}{15}x + \frac{4}{15} \rightarrow y =-\frac{1}{5}x + \frac{4}{15}$

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

$-\frac{1}{5}$

3

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

$\frac{1}{m^3}-\frac{1}{k^2}=\frac{1}{p}$

$m=(\frac{p+k^2}{2})^3$

$m=\frac{p^2k^3}{p+k^2}$

$m=p^{\frac{1}{2}}-k^{\frac{1}{3}}$

$m=(\frac{p+k^2}{pk^2})^{\frac{1}{3}}$

$m=(\frac{pk^2}{p+k^2})^{\frac{1}{3}}$

Explanation

Pkm_7-21-13

Pkm2_7-21-13

4

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?

Explanation

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

$\frac{1}{2} + \frac{1}{3} + x = 1$

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 .

$\frac{1}{2}\cdot \frac{3}{3} = \frac{3}{6}$

$\frac{1}{3}\cdot \frac{2}{2} = \frac{2}{6}$

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

$\frac{3}{6} + \frac{2}{6} + x = 1$

$\frac{5}{6} + x = 1$

$x = \frac{1}{6}$

5

Rational_5

–2

–1

0

1

2

Explanation

Rational_2

Rational_3

Rational_4

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