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Add & Subtract Rational ExpressionsAdd & Subtract Rational Expressions
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Question 1 of 7
1. Question
Perform the operation`(4x)/14 + (6x)/14`Hint
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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
2. Question
Perform the operation`(4m)/(m1) – (m+3)/(m1)`Hint
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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.`(4m)/(m1) – (m+3)/(m1)` `=` `(4m(m+3))/(m1)` `=` `(4mm3)/(m1)` Distribute the negative sign `=` `(3m3)/(m1)` Combine like terms `=` `(3(m1))/(m1)` Factor out `3` from the numerator `=` `3` Cancel out `m1` `3` 
Question 3 of 7
3. Question
Perform the operation`(2m+15)/(m3) – (m1)/(m3)`Hint
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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)/(m3) – (m1)/(m3)` `=` `(2m+15 – (m1))/(m3)` `=` `(2m+15m+1)/(m3)` Distribute negative sign `=` `(m+16)/(m3)` Simplify `(m+16)/(m3)` 
Question 4 of 7
4. Question
Perform the operation`(a9)/(2a+7) – (2a+4)/(2a+7)`Hint
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Excellent!
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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.`(a9)/(2a+7) – (2a+4)/(2a+7)` `=` `(a9 – (2a+4))/(2a+7)` `=` `(a9+2a4)/(2a+7)` Distribute negative sign `=` `(3a13)/(2a+7)` Simplify `(3a13)/(2a+7)` 
Question 5 of 7
5. Question
Perform the operation`4+7/(x+5)`Hint
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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
6. Question
Perform the operation`3x^2+(x+2)/(x^24)`Hint
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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^24)` `=` `3x^2+(x+2)/((x2)(x+2))` `x^24 = (x2)(x+2)` `=` `3x^2+1/(x2)` Cancel out `x+2` `=` `(3x^2)/1+1/(x2)` Write `3x^2` as a fraction $$=$$ $$\frac{3x^2 \times \color{red}{(x2)}}{1 \times \color {red}{(x2)}} + \frac{1}{x2}$$ Multiply `(3x^2)/1` by the LCD `=` `(3x^2(x2))/(x2) + 1/(x2)` Simplify `=` `(3x^2(x2)+1)/(x2)` Combine the numerators `=` `(3x^36x^2+1)/(x2)` Distribute `3x^2` inside parenthesis `(3x^36x^2+1)/(x2)` 
Question 7 of 7
7. Question
Perform the operation`x2+(x+4)/(x5)`Hint
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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.`x2+(x+4)/(x5)` `=` `(x2)/1+(x+4)/(x5)` Convert `x2` into a fraction $$=$$ $$\frac{(x2) \times \color{red}{(x5)}}{1 \times \color {red}{(x5)}} + \frac{x+4}{x5}$$ Multiply `(x2)/1` by the LCD `=` `((x2)(x5))/(x5) + (x+4)/(x5)` Simplify `=` `((x2)(x5)+x+4)/(x5)` Combine the numerators `=` `(x^27x+10+x+4)/(x5)` Distribute `x2` inside parenthesis `=` `(x^26x+14)/(x5)` Simplify `(x^26x+14)/(x5)`