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Multiply & Divide Rational ExpressionsMultiply & Divide Rational Expressions
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Question 1 of 6
1. Question
Multiply`(3x^2)/(4x) xx (5x^2)/(10x^3)`Hint
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Multiplying Rational Expressions
`a/b xx c/d = (ab)/(cd)`Multiply the terms in the numerator and then in the denominator.`(3x^2)/(4x) xx (5x^2)/(10x^3)` `=` `(3x^2 xx 5x^2)/(4x xx 10x^3)` `=` `((3xx5)x^(2+2))/((4xx10) x^(1+3)` Multiply the constants and the variables `=` `(15x^4)/(40x^4)` Apply Multiplication Rule of Exponents `=` `15/40` `=` `3/8` Express in lowest terms `3/8` 
Question 2 of 6
2. Question
Multiply`(m^25m6)/(m2) xx (4m8)/(m6)`Hint
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Multiplying Rational Expressions
`a/b xx c/d = (ab)/(cd)`Look for polynomials that can be factorised before proceeding with the operation. Since the numerator of the first term is in standard form `(``a``x^2+``b``x+``c``=0)` we can factorise using the cross method.`m^2``5``m``6``=0`To factorise, we need to find two numbers that add to `5` and multiply to `6``6` and `1` fit both conditions`6+1` `=` `5` `6 xx 1` `=` `6` Read across to get the factors.`(m6)(m+1)=0`Do the same for the numerator of the second term.`4m8` `=` `4(m2)` Rewrite the expression with the factors.`(m^25m6)/(m2) xx (4m8)/(m6)` `=` `((m6)(m+1))/(m2) xx (4(m2))/(m6)` `=` `(m+1) xx 4` Cancel out `m6` and `m2` `=` `4(m+1)` Simplify `4(m+1)` 
Question 3 of 6
3. Question
Multiply`(4x^2+4x)/(5x^25x60) xx (x^26x+8)/(x^22x)`Hint
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Multiplying Rational Expressions
`a/b xx c/d = (ab)/(cd)`Look for polynomials that can be factorised before proceeding with the operation.`4x^2+4x` `=` `4x(x+1)` `5x^25x60` `=` `5(x^2x12)` `x^22x` `=` `x(x2)` The denominator of the first term is in standard form `(``a``x^2+``b``x+``c``=0)` so we can factorise using the cross method.`x^2````x``12``=0`To factorise, we need to find two numbers that add to `1` and multiply to `12``4` and `3` fit both conditions`4+3` `=` `1` `4 xx 3` `=` `12` Read across to get the factors.`(x4)(x+3)=0`The numerator of the second term is also in standard form `(``a``x^2+``b``x+``c``=0)` so we can factorise using the cross method.`x^2``6``x+``8``=0`To factorise, we need to find two numbers that add to `6` and multiply to `8``4` and `2` fit both conditions`42` `=` `6` `4 xx 2` `=` `8` Read across to get the factors.`(x4)(x2)=0`Rewrite the expression with the factors.`(4x^2+4x)/(5x^25x60) xx (x^26x+8)/(x^22x)` `=` `(4x(x+1))/(5(x4)(x+3)) xx ((x4)(x2))/(x(x2))` `=` `(4(x+1))/(5(x+3))` Cancel out `x`, `x4` and `x2` `(4(x+1))/(5(x+3))` 
Question 4 of 6
4. Question
Divide`(6a^2+11a10)/(3a2) : (2a+5)`Hint
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Dividing Rational Expressions
`a/b : c/d = a/b xx d/c`Since the numerator of the first term is in standard form `(``a``x^2+``b``x+``c``=0)` we can factorise using the cross method.`6``a^2+``11``a``10``=0`To factorise, we need to find two numbers that add to `11` and multiply to `10``3a`, `2a`, `2` and `5` fit both conditions`15a – 4a` `=` `11``a` `2 xx 5` `=` `10` Read across to get the factors.`(3a2)(2a+5)=0`Rewrite the expressions`(6a^2+11a10)/(3a2) : (2a+5)` `=` `((3a2)(2a+5))/(3a2) : (2a+5)` `=` `((3a2)(2a+5))/(3a2) xx 1/(2a+5)` Apply Division Formula `=` `1` `3a2` and `2a+5` cancel out in the denominator `1` 
Question 5 of 6
5. Question
Divide`(3x^29x)/(x^212x+36) : (x^39x)/(x6)`Hint
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Dividing Rational Expressions
`a/b : c/d = a/b xx d/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.`x^2``12``x+``36``=0`To factorise, we need to find two numbers that add to `12` and multiply to `36``6` and `6` fit both conditions`6 – 6` `=` `12` `6 xx 6` `=` `36` Read across to get the factors.`(x6)(x6)=0`Factorise remaining expressions.`3x^29x` `=` `3x(x3)` Factor `3x` out `x^39x` `=` `x(x^29)` Factor `x` out `=` `x(x3)(x+3)` `x^29 = (x3)(x+3)` Rewrite the expressions`(3x^29x)/(x^212x+36) : (x^39x)/(x6)` `=` `(3x^29x)/(x^212x+36) xx (x6)/(x^39x)` Apply Division Formula `=` `(3x(x3))/((x6)(x6)) xx (x6)/(x(x3)(x+3))` Show factors `=` `3/((x6)(x+3))` Cancel out like terms `3/((x6)(x+3))` 
Question 6 of 6
6. Question
Divide`(m^2+2m8)/(m^23m+2) : (m^2+5m+4)/(m^24m+3)`Hint
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Dividing Rational Expressions
`a/b : c/d = a/b xx d/c`Since the given polynomials are in standard form `(``a``x^2+``b``x+``c``=0)` we can factorise using the cross method.`m^2+``2``m``8``=0`To factorise, we need to find two numbers that add to `2` and multiply to `8``4` and `2` fit both conditions`4 – 2` `=` `2` `4 xx 2` `=` `8` Read across to get the factors.`(m+4)(m2)=0`Do the same for the remaining polynomials.`m^2``3``m+``2``=0`To factorise, we need to find two numbers that add to `3` and multiply to `2``2` and `1` fit both conditions`2 – 1` `=` `3` `2 xx 1` `=` `2` Read across to get the factors.`(m2)(m1)=0``m^2+``5``m+``4``=0`To factorise, we need to find two numbers that add to `5` and multiply to `4``4` and `1` fit both conditions`4 + 1` `=` `5` `4 xx 1` `=` `4` Read across to get the factors.`(m+4)(m+1)=0``m^2``4``m+``3``=0`To factorise, we need to find two numbers that add to `4` and multiply to `3``3` and `1` fit both conditions`3 – 1` `=` `4` `3 xx 1` `=` `3` Read across to get the factors.`(m3)(m1)=0`Rewrite the expressions`(m^2+2m8)/(m^23m+2) : (m^2+5m+4)/(m^24m+3)` `=` `(m^2+2m8)/(m^23m+2) xx (m^24m+3)/(m^2+5m+4)` Apply Division Formula `=` `((m+4)(m2))/((m2)(m1)) xx ((m3)(m1))/((m+4)(m+1))` Show factors `=` `(m3)/(m+1)` Cancel out like terms `(m3)/(m+1)`