Add and Subtract Algebraic Fractions

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Question 1 of 7

1. Question
Perform the operation

$(4x)/14 + (6x)/14$
- 1. $(5x)/7$
- 2. $35$
- 3. $-(5x)/7$
- 4. $5x$
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Adding and Subtracting Rational Expressions

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

Since the denominators are the same, we need to perform the operation on the numerators alone.

$(4x)/14 +(6x)/14$ $=$ $(10x)/14$

$=$ $(5x)/7$ Express in lowest terms

$(5x)/7$

Question 2 of 7

Perform the operation

$(4m)/(m-1) – (m+3)/(m-1)$

1. $3m-3$
2. $m-2$
3. $1$
4. $3$

Question 3 of 7

3. Question
Perform the operation

$(2m+15)/(m-3) – (m-1)/(m-3)$
- 1. $(3m+16)/(m-3)$
- 2. $(m-16)/(m-3)$
- 3. $m+16$
- 4. $(m+16)/(m-3)$
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Adding and Subtracting Rational Expressions

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

Since the denominators are the same, we need to perform the operation on the numerators alone.

$(2m+15)/(m-3) – (m-1)/(m-3)$ $=$ $(2m+15 – (m-1))/(m-3)$

$=$ $(2m+15-m+1)/(m-3)$ Distribute negative sign

$=$ $(m+16)/(m-3)$ Simplify

$(m+16)/(m-3)$

Question 4 of 7

Perform the operation

$(a-9)/(2a+7) – (-2a+4)/(2a+7)$

1. $(3a-13)/(2a+7)$
2. $(3a+13)/(2a+7)$
3. $2a+7$
4. $3a-13$

Question 5 of 7

Perform the operation

$4+7/(x+5)$

1. $4x+20$
2. $4$
3. $(4x+27)/(x-5)$
4. $(4x+27)/(x+5)$

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Adding and Subtracting Rational Expressions

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

Rewrite the expressions such that they have the same denominators.

$4+7/(x+5)$	$=$	$4/1+7/(x+5)$	Convert $4$ into a fraction

	$=$	$\frac{4 \times \color{red}{(x+5)}}{1 \times \color {red}{(x+5)}} + \frac{7}{x+5}$	Multiply $4/1$ by the LCD

	$=$	$(4(x+5))/(x+5) + 7/(x+5)$	Simplify

	$=$	$(4(x+5)+7)/(x+5)$	Combine the numerators

	$=$	$(4x+20+7)/(x+5)$	Distribute $4$ inside parenthesis

	$=$	$(4x+27)/(x+5)$	Simplify

$(4x+27)/(x+5)$

Question 6 of 7

Perform the operation

$3x^2+(x+2)/(x^2-4)$

1. $x+2$
2. $(3x^2-6x+1)/(x-2)$
3. $(3x^3-6x^2+1)/(x-2)$
4. $3x^3-6x^2+1$

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Adding and Subtracting Rational Expressions

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

Factorise the denominator of the second term.

$3x^2+(x+2)/(x^2-4)$	$=$	$3x^2+(x+2)/((x-2)(x+2))$	$x^2-4 = (x-2)(x+2)$

	$=$	$3x^2+1/(x-2)$	Cancel out $x+2$

	$=$	$(3x^2)/1+1/(x-2)$	Write $3x^2$ as a fraction

	$=$	$\frac{3x^2 \times \color{red}{(x-2)}}{1 \times \color {red}{(x-2)}} + \frac{1}{x-2}$	Multiply $(3x^2)/1$ by the LCD

	$=$	$(3x^2(x-2))/(x-2) + 1/(x-2)$	Simplify

	$=$	$(3x^2(x-2)+1)/(x-2)$	Combine the numerators

	$=$	$(3x^3-6x^2+1)/(x-2)$	Distribute $3x^2$ inside parenthesis

$(3x^3-6x^2+1)/(x-2)$

Question 7 of 7

Perform the operation

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

1. $(x^2-6x+14)/(x-5)$
2. $(x^2-6x+14)/(x+5)$
3. $(x^2-8x+14)/(x-5)$
4. $(x^2-8x+14)/(x+5)$

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Adding and Subtracting Rational Expressions

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

Rewrite the expressions such that they have the same denominators.

$x-2+(x+4)/(x-5)$	$=$	$(x-2)/1+(x+4)/(x-5)$	Convert $x-2$ into a fraction

	$=$	$\frac{(x-2) \times \color{red}{(x-5)}}{1 \times \color {red}{(x-5)}} + \frac{x+4}{x-5}$	Multiply $(x-2)/1$ by the LCD

	$=$	$((x-2)(x-5))/(x-5) + (x+4)/(x-5)$	Simplify

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

	$=$	$(x^2-7x+10+x+4)/(x-5)$	Distribute $x-2$ inside parenthesis

	$=$	$(x^2-6x+14)/(x-5)$	Simplify

$(x^2-6x+14)/(x-5)$

$(4m)/(m-1) – (m+3)/(m-1)$	$=$	$(4m-(m+3))/(m-1)$

	$=$	$(4m-m-3)/(m-1)$	Distribute the negative sign

	$=$	$(3m-3)/(m-1)$	Combine like terms

	$=$	$(3(m-1))/(m-1)$	Factor out $3$ from the numerator

	$=$	$3$	Cancel out $m-1$

Add and Subtract Algebraic Fractions

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Quiz summary

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1. Question

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Well Done!

Adding and Subtracting Rational Expressions

2. Question

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Great Work!

Adding and Subtracting Rational Expressions

3. Question

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Keep Going!

Adding and Subtracting Rational Expressions

4. Question

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Excellent!

Adding and Subtracting Rational Expressions

5. Question

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Well Done!

Adding and Subtracting Rational Expressions

6. Question

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Nice Job!

Adding and Subtracting Rational Expressions

7. Question

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Fantastic!

Adding and Subtracting Rational Expressions

Quizzes

$(4x)/14 +(6x)/14$	$=$	$(10x)/14$

	$=$	$(5x)/7$	Express in lowest terms

$(2m+15)/(m-3) – (m-1)/(m-3)$	$=$	$(2m+15 – (m-1))/(m-3)$

	$=$	$(2m+15-m+1)/(m-3)$	Distribute negative sign

	$=$	$(m+16)/(m-3)$	Simplify

$(a-9)/(2a+7) – (-2a+4)/(2a+7)$	$=$	$(a-9 – (-2a+4))/(2a+7)$

	$=$	$(a-9+2a-4)/(2a+7)$	Distribute negative sign

	$=$	$(3a-13)/(2a+7)$	Simplify