10 January 2022 Adding and subtracting algebraic fractions

10 January 2022 Adding and subtracting algebraic fractions LO: To use the distributive law to expand brackets. www. mathssupport. org

Subtracting algebraic fractions We can also subtract algebraic fractions using the same method as we use for numerical fractions. For example, p 3 p What is ? + 4 2 We need to write the fractions over a common denominator before we can add them. 3 p 2 p + 2 2 4 Since one denominator is a multiple of the other, we don’t change the fraction with the largest denominator p 6 p change the other fraction = + 4 4 = www. mathssupport. org 7 p 4

Subtracting algebraic fractions We can also subtract algebraic fractions using the same method as we use for numerical fractions. For example, p q What is – ? 3 2 We need to write the fractions over a common denominator before we can subtract them. In general, a c ad – bc – = b d bd p q – 3 2 www. mathssupport. org = 2 p – 3 q 6 2 p – 3 q = 6

Adding algebraic fractions We can add algebraic fractions using the same method that we use for numerical fractions. For example, 1 2 What is + ? a b We need to write the fractions over a common denominator before we can add them. In general, a c ad + bc + = b d bd 1 2 + a b www. mathssupport. org = b + 2 a ab

Subtracting algebraic fractions We can also subtract algebraic fractions using the same method as we use for numerical fractions. For example, 5 4 – What is ? 3 x x We need to write the fractions over a common denominator before we can subtract them. 5 3 4 – x 3 3 x Since one denominator is a multiple of the other, we don’t change the fraction with the largest denominator change the other fraction 15 = – 3 x = www. mathssupport. org 11 3 x 4 3 x

Subtracting algebraic fractions We can also subtract algebraic fractions using the same method as we use for numerical fractions. For example, y 3 What is + ? x 2 We need to write the fractions over a common denominator before we can add them. In general, a c ad + bc + = b d bd y 3 = + x 2 www. mathssupport. org 6 + xy 2 x 6 + xy = 2 x

Subtracting algebraic fractions We can also subtract algebraic fractions using the same method as we use for numerical fractions. For example, b What is + 2 ? 3 We need to write the fractions over a common denominator before we can add them. b + 2 3 We have to write the whole number as a fraction with the same denominator b 6 = + 3 3 = www. mathssupport. org b+6 3

Subtracting algebraic fractions We can also subtract algebraic fractions using the same method as we use for numerical fractions. For example, x – x ? What is 5 We need to write the x as a fraction. x 5 x – 1 5 5 We have to write the two fractions with the same denominator = x 5 4 x =– 5 www. mathssupport. org – 5 x 5

Subtracting algebraic fractions We can also subtract algebraic fractions using the same method as we use for numerical fractions. For example, x x– 2 ? What is + 6 3 We need to write the fractions over a common denominator before we can subtract them. x x – 2 2 + 3 2 6 Since one denominator is a multiple of the other, we don’t change the fraction with the largest denominator change the other fraction www. mathssupport. org 2 x – 4 + 6 = x 6 = 3 x – 4 6

Subtracting algebraic fractions We can also subtract algebraic fractions using the same method as we use for numerical fractions. For example, x– 2 x+ 1 ? – What is 2 3 We need to write the fractions over a common denominator before we can subtract them. In general, a – b ad – bc c = d bd x+ 1 3(x + 1) – 2(x – 2) x– 2 – = 6 2 3 3 x + 3 – 2 x + 4 = 6 x+7 = 6 www. mathssupport. org

Subtracting algebraic fractions We can also subtract algebraic fractions using the same method as we use for numerical fractions. For example, 1 3 ? What is x + x– 2 We need to write the fractions over a common denominator before we can add them. In general, www. mathssupport. org a c ad + bc + = b d bd 1 1(x – 2) + 3(x) 3 x + x– 2 = x (x – 2) + 3 x = x– 2 x (x – 2) 4 x – 2 = x (x – 2)

Subtracting algebraic fractions We can also subtract algebraic fractions using the same method as we use for numerical fractions. For example, 3 2 – What is ? x – 2 x+2 We need to write the fractions over a common denominator before we can subtract them. In general, a – b ad – bc c = d bd 2(x – 2) – 3(x + 2) 3 2 – = x– 2 x+2 (x + 2)(x – 2) 3 x – 6 = 2 x – 4 – (x + 2)( x – 2) –x – 10 = (x + 2)( x – 2) www. mathssupport. org

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