Add and Subtract Algebraic Fractions with Unlike Denominators 2

Years

Try VividMath Premium to unlock full access

Start Free Trial

Lets see your results!

Points

Score

Time

Retry Quiz

Answered
Review

Question 1 of 4

Perform the operation

$4/(3n+6)+n/(n^2-4)$

1. $(7n-8)/(3(n-2)(n+2))$
2. $(4n-8)/(3(n-2)(n+2))$
3. $(7n-8)/(3(n-2))$
4. $(n+2)/(3(n-2)(n+2))$

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

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

First, expand the denominators.

$4/(3n+6)+n/(n^2-4)$

$=$

$4/(3(n+2))+n/((n+2)(n-2))$

Next, identify the LCD.

Since we have different denominators, the LCD would be

$(3)(n+2)(n-2)$ .

Convert into same denominators using the LCD.

$\frac {4}{3n+6}+ \frac {n}{n^2-4}$	$=$	$\frac {4}{3(n+2)}+ \frac {n}{(n-2)(n+2)}$

	$=$	$\frac {4 \times \color{red}{(n-2)}}{3(n+2) \times \color{red}{(n-2)}}+ \frac {n \times \color{red}{3}}{(n-2)(n+2) \times \color {red}{3}}$	LCD is $3(n-2)(n+2)$

	$=$	$(4(n-2))/(3(n-2)(n+2))+ (3n)/(3(n-2)(n+2))$	Simplify

	$=$	$(4(n-2)+3n)/(3(n-2)(n+2))$	Combine numerators

	$=$	$(4n-8+3n)/(3(n-2)(n+2))$	Distribute $4$ inside parenthesis

	$=$	$(7n-8)/(3(n-2)(n+2))$	Combine like terms

$(7n-8)/(3(n-2)(n+2))$

Question 2 of 4

Perform the operation

$5/(4x-8)-(3x)/(x+2)$

1. $(-12x^2+29x+10)/((4x-8)(x+2))$
2. $(-12x^2+29x+10)/(x+2)$
3. $(4x-8)(x+2)$
4. $-12x^2+29x+10$

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

$(4x-8)(x+2)$ .

Convert into same denominators using the LCD.

$\frac {5}{4x-8}- \frac {3x}{x+2}$	$=$	$\frac {5 \times \color{red}{(x+2)}}{(4x-8) \times \color {red}{(x+2)}}- \frac {3x \times \color{red}{(4x-8)}}{(x+2) \times \color{red}{(4x-8)}}$	LCD is $(4x-8)(x+2)$

	$=$	$(5(x+2)-3x(4x-8))/((4x-8)(x+2))$	Combine the numerators

	$=$	$(5x+10-12x^2+24x)/((4x-8)(x+2))$	Distribute the terms inside parenthesis

	$=$	$(-12x^2+29x+10)/((4x-8)(x+2))$	Combine like terms

$(-12x^2+29x+10)/((4x-8)(x+2))$

Question 3 of 4

Perform the operation

$(3m+1)/(m-1)^2-(m-2)/(m^2+4m-5)$

1. $4m^2-13m-7$
2. $(4m^2+13m+7)/((m-1)(m-1)(m+5))$
3. $(4m^2+13m+7)/((m-1)(m+5))$
4. $(m-1)(m-1)(m+5)$

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, expand the denominators starting with the first term.

$(3m+1)/(m-1)^2-(m-2)/(m^2+4m-5)$

$=$

$(3m+1)/((m-1)(m-1))-(m-2)/(m^2+4m-5)$

Since the denominator of the second term is in standard form

$($ $a$

$x^2+$ $b$

$x+$ $c$

$=0)$ we can factorise using the cross method.

$m^2+$ $4$

$m$ $-5$

$=0$

To factorise, we need to find two numbers that add to $4$ and multiply to $-5$

$5$ and

$-1$ fit both conditions

$5 – 1$	$=$	$4$
$5 xx -1$	$=$	$-5$

Read across to get the factors.

$(m+5)(m-1)=0$

Copy the factors of

$m^2+4m-5$ .

$(3m+1)/(m-1)^2-(m-2)/(m^2+4m-5)$

$=$

$(3m+1)/((m-1)(m-1))-(m-2)/((m+5)(m-1))$

Next, identify the LCD.

$m-1$ is common in the denominators, so the LCD would be

$(m-1)(m-1)(m+5)$ .

Convert into same denominators using the LCD.

$=$	$\frac {(3m+1) \times \color{red}{(m+5)}}{(m-1)(m-1) \times \color{red}{(m+5)}}+ \frac {(m-2) \times \color{red}{(m-1)}}{(m+5)(m-1) \times \color{red}{(m-1)}}$	LCD is $(m-1)(m-1)(m+5)$

$=$	$((3m+1)(m+5)+(m-2)(m-1))/((m-1)(m-1)(m+5))$	Combine the numerators

$=$	$((3m^2+16m+5)+(m^2-3m+2))/((m-1)(m-1)(m+5))$	Distribute the terms

$=$	$(4m^2+13m+7)/((m-1)(m-1)(m+5))$	Combine like terms

$(4m^2+13m+7)/((m-1)(m-1)(m+5))$

Question 4 of 4

Perform the operation

$(a-3)/(a^2+6a+9)-(a+3)/(a-3)$

1. $(-a^3-8a^2-33a-18)/((a+3)(a+3)(a-3))$
2. $(a^3+8a^2+33a-18)/((a+3)(a+3)(a-3))$
3. $(a+3)(a+3)(a-3)$
4. $-a^3-8a^2-33a-18$

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

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

Since the denominator of the first term is in standard form

$($ $a$

$x^2+$ $b$

$x+$ $c$

$=0)$ we can factorise using the cross method.

$a^2+$ $6$

$a+$ $9$

$=0$

To factorise, we need to find two numbers that add to $6$ and multiply to $9$

$3$ and

$-3$ fit both conditions

$3 + 3$	$=$	$6$
$3 xx 3$	$=$	$9$

Read across to get the factors.

$(a+3)(a+3)=0$

Copy the factors to the original expression.

$(a-3)/(a^2+6a+9)-(a+3)/(a-3)$

$=$

$(a-3)/((a+3)(a+3))-(a+3)/(a-3)$

Next, identify the LCD.

There is no common term in the denominators, so the LCD would be

$(a+3)(a+3)(a-3)$ .

Convert into same denominators using the LCD.

$\frac {a-3}{a^2+6a+9}- \frac {a+3}{a-3}$	$=$	$\frac {(a-3) \times \color{red}{(a-3)}}{(a+3)(a+3) \times \color {red}{(a-3)}}- \frac {(a+3) \times \color{red}{(a+3)(a+3)}}{(a-3) \times \color{red}{(a+3)(a+3)}}$	Multiply to come up with same denominators

	$=$	$((a-3)(a-3)-(a+3)(a+3)(a+3))/((a+3)(a+3)(a-3))$

	$=$	$((a^2-6a+9)-(a^3+9a^2+27a+27))/((a+3)(a+3)(a-3))$	Distribute the factors

	$=$	$(a^2-6a+9-a^3-9a^2-27a-27)/((a+3)(a+3)(a-3))$	Distribute the negative sign

	$=$	$(-a^3-8a^2-33a-18)/((a+3)(a+3)(a-3))$	Combine like terms

$(-a^3-8a^2-33a-18)/((a+3)(a+3)(a-3))$

Add and Subtract Algebraic Fractions with Unlike Denominators 2

Try VividMath Premium to unlock full access

Quiz summary

Information

1. Question

Hint

Excellent!

Adding and Subtracting Rational Expressions

2. Question

Hint

Fantastic!

Adding and Subtracting Rational Expressions

3. Question

Hint

Great Work!

Adding and Subtracting Rational Expressions

4. Question

Hint

Exceptional!

Adding and Subtracting Rational Expressions

Quizzes