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Add & Subtract Rational Expressions with Unlike Denominators 1Add & Subtract Rational Expressions with Unlike Denominators 1
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Question 1 of 4
1. Question
Perform the operation`(3x)/(x8)+(5x)/(8x)`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.`x8` `=` `(8x)` $$\frac{3x}{x8}+ \frac{5x}{8x}$$ $$=$$ $$\frac{3x}{x8}+ \frac{5x \times \color {red}{1}}{(8x) \times \color{red}{1}}$$ Change `8x` to `x8` `=` `(3x)/(x8) – (5x)/(x8)` Simplify `=` `(3x5x)/(x8)` Combine the numerators `=` `(2x)/(x8)` `(2x)/(x8)` 
Question 2 of 4
2. Question
Perform the operation`(13)/(n^216)+(5)/(4n)`Hint
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Adding and Subtracting Rational Expressions
`a/c + b/c = (a+b)/c`Expand the denominator of the first term.`(13)/(n^216)+(5)/(4n)` `=` `(13)/((n4)(n+4))+(5)/(4n)` `n^216 = (n4)(n+4)` `=` `(13)/((n4)(n+4))+(5)/(n4)` `4n = – (n4)` Multiply the second term by `(n+4)/(n+4)`$$\frac {13}{n^216}+ \frac{5}{4n}$$ $$=$$ $$\frac{13}{(n4)(n+4)}+ \frac{5 \times \color{red}{(n+4)}}{(n4) \times \color {red}{(n+4)}}$$ `=` `(13)/((n4)(n+4))+(5(n+4))/((n4))(n+4)` Simplify `=` `(13 +5(n+4))/((n4)(n+4))` Combine the numerators `=` `(13 +5n + 20)/((n4)(n+4))` Distribute `5` inside parenthesis `=` `(5n+33)/((n4)(n+4))` Simplify `=` `(5n+33)/(n^216)` `(5n+33)/(n^216)` 
Question 3 of 4
3. Question
Perform the operation`(5x)/(8y)+(3x)/(24y^2)`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.`(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 `=` `(15xy3x)/((8y)(3y))` `=` `(3(5xyx))/((8y)(3y))` Factor out `3` from numerator `=` `(5xyx)/((8y)y)` Cancel out `3` `=` `(5xyx)/(8y^2)` Simplify `(5xyx)/(8y^2)` 
Question 4 of 4
4. Question
Perform the operation`1/(a1)1/a`Hint
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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)(a1)`.Convert into same denominators using the LCD.$$\frac {1}{a1} \frac {1}{a}$$ $$=$$ $$\frac {1 \times \color{red}{a}}{(a1) \times \color {red}{a}} \frac {1 \times \color{red}{(a1)}}{a \times \color{red}{(a1)}}$$ LCD is `a(a1)` `=` `a/(a(a1))(a1)/(a(a1))` Simplify `=` `(a(a1))/(a(a1))` Combine the numerators `=` `(aa+1)/(a(a1))` Distribute the negative sign `=` `1/(a(a1))` `1/(a(a1))`