OCR MEI C4 — Question 8 3 marks

Exam BoardOCR MEI
ModuleC4 (Core Mathematics 4)
Marks3
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicPartial Fractions
TypeSimplify algebraic fractions by addition or subtraction
DifficultyEasy -1.2 This is a straightforward algebraic manipulation requiring factorisation of a difference of squares and finding a common denominator. It's simpler than a typical partial fractions question (which would go the opposite direction) and requires only routine algebraic skills with no problem-solving insight needed.
Spec1.02k Simplify rational expressions: factorising, cancelling, algebraic division
8 Express \(\frac { x } { x ^ { 2 } - 4 } + \frac { 2 } { x + 2 }\) as a single fraction, simplifying your answer.
Question 8:
AnswerMarks Guidance
\[\frac{2x}{x^2-4} + \frac{x}{x+2} = \frac{2}{(x-2)(x+2)} \cdot x\]M1 combining fractions correctly
\[= \frac{x \cdot 2(+2)}{(x+2)(x-2)}\]M1 factorising and cancelling (may be \(3x^2+2x-8\))
\[= \frac{3x-4}{(x+2)(x-2)}\]A1 [3] 
## Question 8:

$$\frac{2x}{x^2-4} + \frac{x}{x+2} = \frac{2}{(x-2)(x+2)} \cdot x$$ | M1 | combining fractions correctly |

$$= \frac{x \cdot 2(+2)}{(x+2)(x-2)}$$ | M1 | factorising and cancelling (may be $3x^2+2x-8$) |

$$= \frac{3x-4}{(x+2)(x-2)}$$ | A1 [3] | |

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8 Express $\frac { x } { x ^ { 2 } - 4 } + \frac { 2 } { x + 2 }$ as a single fraction, simplifying your answer.

\hfill \mbox{\textit{OCR MEI C4  Q8 [3]}}
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Q1 5 Q2 5 Q3 5 Q4 5 Q5 3 Q6 5 Q7 8 Q8 3 Q9 8 Q10 8