GCSE Edexcel Maths Algebraic Fractions: 2 \( \frac{x + 2}{x - 3}

2 $ \frac{x + 2}{x - 3} - \frac{x - 6}{x + 3} $ can be written as a single fraction in the form $ \frac{ax + b}{x^2 - 9} $ where a and b are integers - Edexcel - GCSE Maths - Question 19 - 2017 - Paper 2

Question 19

$2-$-\frac{x-+-2}{x---3}---\frac{x---6}{x-+-3}-$-can-be-written-as-a-single-fraction-in-the-form-$-\frac{ax-+-b}{x^2---9}-$-where-a-and-b-are-integers-Edexcel-GCSE Maths-Question 19-2017-Paper 2.png$

2 $ \frac{x + 2}{x - 3} - \frac{x - 6}{x + 3} $ can be written as a single fraction in the form $ \frac{ax + b}{x^2 - 9} $ where a and b are integers. Work out ... show full transcript

Worked Solution & Example Answer:2 $ \frac{x + 2}{x - 3} - \frac{x - 6}{x + 3} $ can be written as a single fraction in the form $ \frac{ax + b}{x^2 - 9} $ where a and b are integers - Edexcel - GCSE Maths - Question 19 - 2017 - Paper 2

Step 1

Combine the Fractions

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Answer

To combine the fractions, we first find a common denominator, which in this case is ( (x - 3)(x + 3) = x^2 - 9 ).

The expression then becomes:

$\frac{(x + 2)(x + 3) - (x - 6)(x - 3)}{x^2 - 9}$

Step 2

Simplify the Numerator

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Answer

Next, we expand both terms in the numerator:

( (x + 2)(x + 3) = x^2 + 3x + 2x + 6 = x^2 + 5x + 6 )

( (x - 6)(x - 3) = x^2 - 3x - 6x + 18 = x^2 - 9x + 18 )

Therefore, the combined numerator is:

( (x^2 + 5x + 6) - (x^2 - 9x + 18) = x^2 + 5x + 6 - x^2 + 9x - 18 )

This simplifies to:

( 14x - 12 )

Step 3

Express in Required Form

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Answer

Now, substituting back into our combined fraction, we have:

$\frac{14x - 12}{x^2 - 9}$

This matches the required form ( \frac{ax + b}{x^2 - 9} ), where ( a = 14 ) and ( b = -12 ).

2 \( \frac{x + 2}{x - 3} - \frac{x - 6}{x + 3} \) can be written as a single fraction in the form \( \frac{ax + b}{x^2 - 9} \) where a and b are integers - Edexcel - GCSE Maths - Question 19 - 2017 - Paper 2

Worked Solution & Example Answer:2 \( \frac{x + 2}{x - 3} - \frac{x - 6}{x + 3} \) can be written as a single fraction in the form \( \frac{ax + b}{x^2 - 9} \) where a and b are integers - Edexcel - GCSE Maths - Question 19 - 2017 - Paper 2

Combine the Fractions

Simplify the Numerator

Express in Required Form

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