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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)/(m-1) – (m+3)/(m-1)`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)/(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` `3` -
Question 3 of 7
3. Question
Perform the operation`(2m+15)/(m-3) – (m-1)/(m-3)`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)/(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
4. Question
Perform the operation`(a-9)/(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.`(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 `(3a-13)/(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^2-4)`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^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
7. Question
Perform the operation`x-2+(x+4)/(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.`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)`