2x + 3 ────────── + x - 4 x - 5 x + 5 - 3 can be written in the form ax + b ─────────── where a and b are integers. x² - 25 Work out the value of a and the value of b. You must show all your working. a = ___________ b = ___________

GCSE Edexcel Maths Rearranging Formulae: 2x + 3 ────────── + x

2x + 3 ────────── + x - 4 x - 5 x + 5 - 3 can be written in the form ax + b ─────────── where a and b are integers - Edexcel - GCSE Maths - Question 22 - 2022 - Paper 3

Question 22

2x + 3 ────────── + x - 4 x - 5 x + 5 - 3 can be written in the form ax + b ─────────── where a and b are integers. x² - 25 ... show full transcript

Worked Solution & Example Answer:2x + 3 ────────── + x - 4 x - 5 x + 5 - 3 can be written in the form ax + b ─────────── where a and b are integers - Edexcel - GCSE Maths - Question 22 - 2022 - Paper 3

Step 1

Step 1: Combine the Fractions

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Answer

First, let's rewrite the left-hand side:

$rac{2x + 3}{x - 5} + rac{x - 4}{x + 5} - 3$

To combine these fractions, we need a common denominator which is ((x - 5)(x + 5) = x^2 - 25).

Step 2

Step 2: Simplify the Expression

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Answer

Rewriting the fractions:

$rac{(2x + 3)(x + 5) + (x - 4)(x - 5) - 3(x - 5)(x + 5)}{x^2 - 25}$

Expanding each term:

((2x + 3)(x + 5) = 2x^2 + 10x + 3x + 15 = 2x^2 + 13x + 15)
((x - 4)(x - 5) = x^2 - 5x - 4x + 20 = x^2 - 9x + 20)
(-3(x^2 - 25) = -3x^2 + 75)

Combine these:

$2x^2 + 13x + 15 + x^2 - 9x + 20 - 3x^2 + 75$

This simplifies to:

$(-x^2 + 4x + 110)$

Step 3

Step 3: Set Up for a and b

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Answer

We can now express the original fraction as:

$\frac{-x^2 + 4x + 110}{x^2 - 25}$

This means that:

a = 4

b = 110

2x + 3 ────────── + x - 4 x - 5 x + 5 - 3 can be written in the form ax + b ─────────── where a and b are integers - Edexcel - GCSE Maths - Question 22 - 2022 - Paper 3

Worked Solution & Example Answer:2x + 3 ────────── + x - 4 x - 5 x + 5 - 3 can be written in the form ax + b ─────────── where a and b are integers - Edexcel - GCSE Maths - Question 22 - 2022 - Paper 3

Step 1: Combine the Fractions

Step 2: Simplify the Expression

Step 3: Set Up for a and b

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