Add & Subtract Rational Expressions with Unlike Denominators 1

Quiz summary

0 of 4 questions completed

Questions:

–

You have already completed the quiz before. Hence you can not start it again.

Quiz is loading...

You must sign in or sign up to start the quiz.

You have to finish following quiz, to start this quiz:

Lets see your results!

Points

Score

Time

Retry Quiz

Question 1 of 4

Perform the operation

$(3x)/(x-8)+(5x)/(8-x)$

1. $x-8$
2. $(x-8)/(2x)$
3. $(2x)/(x-8)$
4. $(-2x)/(x-8)$

Incorrect

Need Text

Play

Remaining Time -0:00

Stream TypeLIVE

Loaded: 0%

Progress: 0%

0:00

Fullscreen

00:00

Mute

Adding and Subtracting Rational Expressions

$a/c +- b/c = (a+-b)/c$

Rewrite the expressions such that they have the same denominators.

$x-8$	$=$	$-(8-x)$

$\frac{3x}{x-8}+ \frac{5x}{8-x}$	$=$	$\frac{3x}{x-8}+ \frac{5x \times \color {red}{-1}}{(8-x) \times \color{red}{-1}}$	Change $8-x$ to $x-8$

	$=$	$(3x)/(x-8) – (5x)/(x-8)$	Simplify

	$=$	$(3x-5x)/(x-8)$	Combine the numerators

	$=$	$(-2x)/(x-8)$

$(-2x)/(x-8)$

Question 2 of 4

Perform the operation

$(13)/(n^2-16)+(-5)/(4-n)$

1. $n+4$
2. $5n+17$
3. $(5n+33)/(n-4)$
4. $(5n+33)/(n^2-16)$

Incorrect

Need Text

Play

Remaining Time -0:00

Stream TypeLIVE

Loaded: 0%

Progress: 0%

0:00

Fullscreen

00:00

Mute

Adding and Subtracting Rational Expressions

$a/c +- b/c = (a+-b)/c$

Expand the denominator of the first term.

$(13)/(n^2-16)+(-5)/(4-n)$	$=$	$(13)/((n-4)(n+4))+(-5)/(4-n)$	$n^2-16 = (n-4)(n+4)$

	$=$	$(13)/((n-4)(n+4))+(5)/(n-4)$	$4-n = – (n-4)$

Multiply the second term by

$(n+4)/(n+4)$

$\frac {13}{n^2-16}+ \frac{-5}{4-n}$	$=$	$\frac{13}{(n-4)(n+4)}+ \frac{5 \times \color{red}{(n+4)}}{(n-4) \times \color {red}{(n+4)}}$

	$=$	$(13)/((n-4)(n+4))+(5(n+4))/((n-4))(n+4)$	Simplify

	$=$	$(13 +5(n+4))/((n-4)(n+4))$	Combine the numerators

	$=$	$(13 +5n + 20)/((n-4)(n+4))$	Distribute $5$ inside parenthesis

	$=$	$(5n+33)/((n-4)(n+4))$	Simplify

	$=$	$(5n+33)/(n^2-16)$

$(5n+33)/(n^2-16)$

Question 3 of 4

Perform the operation

$(5x)/(8y)+(3x)/(24y^2)$

1. $(5xy+x)/(8y^2)$
2. $5xy-x$
3. $(5xy-x)/(8y^2)$
4. $(15xy-3x)/(8y^2)$

Incorrect

Need Text

Play

Remaining Time -0:00

Stream TypeLIVE

Loaded: 0%

Progress: 0%

0:00

Fullscreen

00:00

Mute

Adding and Subtracting Rational Expressions

$a/c +- b/c = (a+-b)/c$

Rewrite the expressions such that they have the same denominators.

$(5x)/(8y)-(3x)/(24y^2)$	$=$	$(5x)/(8y)+(3x)/((8y)(3y))$	$24y^2 = (8y)(3y)$

	$=$	$\frac{5x \times \color{red}{3y}}{8y \times \color {red}{3y}}- \frac {3x}{(8y)(3y)}$	Multiply the first term by $(3y)/(3y)$

	$=$	$(15xy)/((8y)(3y))-(3x)/((8y)(3y))$	Simplify

	$=$	$(15xy-3x)/((8y)(3y))$

	$=$	$(3(5xy-x))/((8y)(3y))$	Factor out $3$ from numerator

	$=$	$(5xy-x)/((8y)y)$	Cancel out $3$

	$=$	$(5xy-x)/(8y^2)$	Simplify

$(5xy-x)/(8y^2)$

Question 4 of 4

Perform the operation

$1/(a-1)-1/a$

1. $a-1$
2. $1/(a(a-1))$
3. $1$
4. $a(a-1)$

Incorrect

Need Text

Play

Remaining Time -0:00

Stream TypeLIVE

Loaded: 0%

Progress: 0%

0:00

Fullscreen

00:00

Mute

Adding and Subtracting Rational Expressions

$a/c +- b/c = (a+-b)/c$

First, identify the LCD.

Since we have different denominators, the LCD would be

$(a)(a-1)$ .

Convert into same denominators using the LCD.

$\frac {1}{a-1}- \frac {1}{a}$	$=$	$\frac {1 \times \color{red}{a}}{(a-1) \times \color {red}{a}}- \frac {1 \times \color{red}{(a-1)}}{a \times \color{red}{(a-1)}}$	LCD is $a(a-1)$

	$=$	$a/(a(a-1))-(a-1)/(a(a-1))$	Simplify

	$=$	$(a-(a-1))/(a(a-1))$	Combine the numerators

	$=$	$(a-a+1)/(a(a-1))$	Distribute the negative sign

	$=$	$1/(a(a-1))$

$1/(a(a-1))$

Add & Subtract Rational Expressions with Unlike Denominators 1

Try VividMath Premium to unlock full access

Quiz summary

Information

1. Question

Hint

Correct!

Adding and Subtracting Rational Expressions

2. Question

Hint

Well Done!

Adding and Subtracting Rational Expressions

3. Question

Hint

Correct!

Adding and Subtracting Rational Expressions

4. Question

Hint

Nice Job!

Adding and Subtracting Rational Expressions

Quizzes