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21 Write as a single fraction in its simplest form - OCR - GCSE Maths - Question 21 - 2020 - Paper 6
Question 21
21 Write as a single fraction in its simplest form. \[ \frac{x}{x + 1} + \frac{6x}{x + 2} - \frac{x - 2}{x^2 - 4} \]
Worked Solution & Example Answer:21 Write as a single fraction in its simplest form - OCR - GCSE Maths - Question 21 - 2020 - Paper 6
Step 1
Finding a Common Denominator
Step 2
Rewriting Fractions
Answer
We will rewrite each fraction with the common denominator:
- ( \frac{x}{x + 1} = \frac{x(x + 2)(x - 2)}{(x + 1)(x + 2)(x - 2)} )
- ( \frac{6x}{x + 2} = \frac{6x(x + 1)(x - 2)}{(x + 1)(x + 2)(x - 2)} )
- ( \frac{x - 2}{x^2 - 4} = \frac{x - 2}{(x - 2)(x + 2)} = \frac{1}{x + 2} ) so we rewrite it as ( \frac{(x + 1)(x - 2)}{(x + 1)(x + 2)(x - 2)} ).
Step 3
Step 4
Simplifying the Numerator
Step 5
Final Expression
Answer
Finally, combine the simplified numerator with the common denominator: [ \frac{x^3 + 6x^3 - 4x - 6x^2 - 12x + x + 2}{(x + 1)(x + 2)(x - 2)} ] Combine like terms to get your final answer in simplest form.