Algebraic Fractions, subtraction #3 - interactive learning from GCSE Maths Tutor

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Algebraic Fractions - Subtraction #3

Worked Solution #3 of 3, increasing in difficulty.

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\begin{align} \quad\quad\quad\quad\quad\quad\quad\quad\Large { \frac{\color{#0000FF}{2x}}{\color{#CC0000}{5y + 3}} - \frac{\color{#0000FF}{3y - 2}}{\color{#CC0000}{x}} }\\ \\ &\cssId{Step1}{\Large = \frac{( \quad \ )( \quad \ ) - ( \quad \ )( \quad \ ) }{( \ \color{#CC0000}{5y + 3} \ )( \ \color{#CC0000}{x} \ ) } }\\ \\ &\cssId{Step2}{\Large = \frac{( \quad \ )( \quad \ ) - ( \quad \ )( \quad \ ) }{\color{#CC0000}{5xy + 3x} } }\\ \\ &\cssId{Step3}{\Large = \frac{ ( \ \color{#0000FF}{2x} \ )( \ \color{#CC0000}{x} \ ) - ( \quad \ )( \quad \ ) }{\color{#CC0000}{5xy + 3x} } }\\ \\ &\cssId{Step4}{\Large = \frac{ ( \ \color{#0000FF}{2x} \ )( \ \color{#CC0000}{x} \ ) - ( \ \color{#0000FF}{3y - 2} \ )( \ \color{#CC0000}{5y + 3} \ ) }{\color{#CC0000}{5xy + 3x} } }\\ \\ &\cssId{Step5}{\Large = \frac{ 2x^2 - ( \ 15y^2 - 10y + 9y - 6 \ ) }{5xy + 3x} }\\ \\ &\cssId{Step6}{\Large = \frac{ 2x^2 - 15y^2 + 10y - 9y + 6 }{5xy + 3x} }\\ \\ &\cssId{Step7}{\Large = \frac{ 2x^2 - 15y^2 + y + 6 }{5xy + 3x} }\\ \\ \end{align}

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numerators $ \quad \color{#0000FF}{n_1} \ , \color{#0000FF}{n_2} \ $

denominators $ \quad \color{#CC0000}{d_1} \ , \ \color{#CC0000}{d_2} \ $

$$ \quad \quad \quad \quad \ \ \ \ \frac{\color{#0000FF}{n_1}}{\color{#CC0000}{d_1}} - \frac{\color{#0000FF}{n_2}}{\color{#CC0000}{d_2}} $$

$$ \ = \frac{( \ \color{#0000FF}{n_1} \ )( \ \color{#CC0000}{d_2} \ ) - ( \ \color{#0000FF}{n_2} \ )( \ \color{#CC0000}{d_1} \ )}{( \ \color{#CC0000}{d_1} \ )( \ \color{#CC0000}{d_2} \ )} $$

1. Draw a horizontal line under the algebraic fraction.

2. Write the common denominator (d1)(d2) under the line.

3. Divide the denominator d1 (from the left-hand fraction) into the common denominator (d1)(d2) to get the answer d2 .

4. Multiply the numerator n1 (from the left-hand fraction) by d2, putting the answer above the line.

5. Divide the denominator d2 (from the right-hand fraction) into the common denominator (d1)(d2) to get the answer d1 .

6. Multiply the numerator n2 (from the right-hand fraction) by d1, putting the answer above the line and subtracted from the left-hand fraction result.

7. Add the terms above the line.

8. Cancel terms above and below the line

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2. Write the common denominator (d₁)(d₂) under the line.

3. Divide the denominator d₁ (from the left-hand fraction) into the common denominator (d₁)(d₂) to get the answer d₂ .

4. Multiply the numerator n₁ (from the left-hand fraction) by d₂, putting the answer above the line.

5. Divide the denominator d₂ (from the right-hand fraction) into the common denominator (d₁)(d₂) to get the answer d₁ .

6. Multiply the numerator n₂ (from the right-hand fraction) by d₁, putting the answer above the line and subtracted from the left-hand fraction result.