A-Level Edexcel Maths Pure Applications of Differentiation: Express \[ \frac{2x^2 + 3x}{(2x

Express \[ \frac{2x^2 + 3x}{(2x + 3)(x - 2)} \div \frac{6}{x^2 - x - 2} \] as a single fraction in its simplest form. - Edexcel - A-Level Maths Pure - Question 4 - 2006 - Paper 5

Question 4

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Express \[ \frac{2x^2 + 3x}{(2x + 3)(x - 2)} \div \frac{6}{x^2 - x - 2} \] as a single fraction in its simplest form.

Worked Solution & Example Answer:Express \[ \frac{2x^2 + 3x}{(2x + 3)(x - 2)} \div \frac{6}{x^2 - x - 2} \] as a single fraction in its simplest form. - Edexcel - A-Level Maths Pure - Question 4 - 2006 - Paper 5

Step 1

Factor the Denominators

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Answer

First, we need to factor the denominator of the second fraction:

[ x^2 - x - 2 = (x - 2)(x + 1) ]

Thus, we can rewrite the original expression as:

[ \frac{2x^2 + 3x}{(2x + 3)(x - 2)} \div \frac{6}{(x - 2)(x + 1)} ]

Step 2

Convert Division to Multiplication

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Answer

We convert the division into multiplication by flipping the second fraction:

[ \frac{2x^2 + 3x}{(2x + 3)(x - 2)} \times \frac{(x - 2)(x + 1)}{6} ]

Step 3

Cancel Common Terms

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Answer

Now, we can cancel the common term ( (x - 2) ) in the numerator and denominator:

[ \frac{2x^2 + 3x}{(2x + 3)} \times \frac{(x + 1)}{6} ]

Step 4

Simplify the Numerator

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Answer

Next, we simplify the numerator ( 2x^2 + 3x ) by factoring:

[ 2x^2 + 3x = x(2x + 3) ]

So now we have:

[ \frac{x(2x + 3)(x + 1)}{(2x + 3) imes 6} ]

Step 5

Cancel the Remaining Common Terms

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Answer

We can cancel ( (2x + 3) ) from the numerator and denominator:

[ \frac{x(x + 1)}{6} ]

Step 6

Final Result

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Answer

Therefore, the resulting expression as a single fraction in its simplest form is:

[ \frac{x(x + 1)}{6} ]

Express \[ \frac{2x^2 + 3x}{(2x + 3)(x - 2)} \div \frac{6}{x^2 - x - 2} \] as a single fraction in its simplest form. - Edexcel - A-Level Maths Pure - Question 4 - 2006 - Paper 5

Worked Solution & Example Answer:Express \[ \frac{2x^2 + 3x}{(2x + 3)(x - 2)} \div \frac{6}{x^2 - x - 2} \] as a single fraction in its simplest form. - Edexcel - A-Level Maths Pure - Question 4 - 2006 - Paper 5

Factor the Denominators

Convert Division to Multiplication

Cancel Common Terms

Simplify the Numerator

Cancel the Remaining Common Terms

Final Result

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