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1.5.6 Polynomials and rational expressions

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Question 30

Given that $n$ is a positive integer, express

\frac{5}{2+3\sqrt{n}} - \frac{5}{3\sqrt{n}-2}

as a single fraction not involving surds.

[5]

Hence, deduce that

\frac{5}{2+3\sqrt{n}} - \frac{5}{3\sqrt{n}-2}

is a rational number for all positive integer values of $n$ .

[2]

Markscheme

1.5.6 Polynomials and rational expressions Questions

A Level
Maths
1.5.6 Polynomials and rational expressions

113 exam-style questions on AQA A Level Maths 1.5.6 Polynomials and rational expressions. Each one has a worked solution and a mark scheme showing where the marks go.

1.5.6 Polynomials and rational expressions

Question bank

1.5.6 Polynomials and rational expressions

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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57

Question 30

Given that $n$ is a positive integer, express

\frac{5}{2+3\sqrt{n}} - \frac{5}{3\sqrt{n}-2}

as a single fraction not involving surds.

[5]

Hence, deduce that

\frac{5}{2+3\sqrt{n}} - \frac{5}{3\sqrt{n}-2}

is a rational number for all positive integer values of $n$ .

[2]

Markscheme

1.5.6 Polynomials and rational expressions Questions

A Level
Maths
1.5.6 Polynomials and rational expressions

113 exam-style questions on AQA A Level Maths 1.5.6 Polynomials and rational expressions. Each one has a worked solution and a mark scheme showing where the marks go.