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Algebraic Fractions (Cambridge O Level Maths)

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Algebraic Fractions

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Algebraic Fractions

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1
Sme Calculator3 marks

Simplify.

fraction numerator 3 over denominator x space minus space 1 end fraction minus fraction numerator 2 over denominator 2 x space plus space 1 end fraction

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2
Sme Calculator2 marks

Simplify.

fraction numerator 5 over denominator 3 x end fraction cross times fraction numerator 9 x over denominator 20 end fraction

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3
Sme Calculator3 marks

Simplify.

fraction numerator x squared plus 5 x over denominator x squared minus 25 end fraction

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4
Sme Calculator3 marks

Write as a single fraction in its simplest form.

fraction numerator x minus 5 over denominator 3 end fraction plus fraction numerator 6 over denominator x plus 2 end fraction

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5
Sme Calculator3 marks

Simplify space fraction numerator x squared minus 25 over denominator x squared minus 2 x minus 35 end fraction.

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6
Sme Calculator3 marks

Write space fraction numerator x minus 8 over denominator x end fraction plus fraction numerator 3 x over denominator x plus 1 end fraction space as a single fraction in its simplest form.

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7
Sme Calculator3 marks

Express as a single fraction in its simplest form fraction numerator 7 over denominator p plus 2 end fraction space minus space fraction numerator 4 over denominator 2 p minus 3 end fraction.

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1
Sme Calculator3 marks

Simplify.

fraction numerator 5 p squared space minus space 20 p over denominator 2 p squared space minus space 32 end fraction

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2
Sme Calculator4 marks

Simplify fraction numerator x squared minus 25 over denominator x squared minus 17 x plus 60 end fraction.

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3
Sme Calculator3 marks

straight f open parentheses x close parentheses equals 7 x minus 4  and  straight g open parentheses x close parentheses equals fraction numerator 2 x over denominator x minus 3 end fraction comma space x not equal to 3 

Find space fraction numerator straight f open parentheses x close parentheses space over denominator 2 end fraction plus straight g open parentheses x close parentheses.
Give your answer as a single fraction, in terms of x, in its simplest form.

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4
Sme Calculator3 marks

Write  x over 2 minus fraction numerator 2 x plus 4 over denominator x plus 1 end fraction  as a single fraction, in its simplest form.

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5
Sme Calculator7 marks

Solve.

1 over x minus fraction numerator 2 over denominator x plus 1 end fraction equals 3

Show all your working and give your answers correct to 2 decimal places.


x = .......................... or x = .......................... 

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6
Sme Calculator3 marks

straight f left parenthesis x right parenthesis equals fraction numerator 3 over denominator x plus 2 end fraction comma space x not equal to negative 2  and  straight g open parentheses x close parentheses equals 8 x minus 5.
 
Write  straight g left parenthesis x right parenthesis minus straight f left parenthesis x right parenthesis as a single fraction in its simplest form.

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7
Sme Calculator4 marks

Simplify.

fraction numerator 2 x squared minus x minus 1 over denominator 2 x squared plus x end fraction

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8
Sme Calculator3 marks

Simplify fraction numerator y squared space minus space 9 over denominator 2 y squared minus y minus 15 end fraction

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1
Sme Calculator5 marks

Simplify fraction numerator 2 x squared plus x minus 15 over denominator a x plus 3 a minus 2 b x minus 6 b end fraction.

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2
Sme Calculator6 marks

A car completes a 200 km journey at an average speed of x km/h.
The car completes the return journey of 200 km at an average speed of left parenthesis x space plus space 10 right parenthesis km/h.

i)
Show that the difference between the time taken for each of the two journeys is  fraction numerator 2000 over denominator x left parenthesis x space plus space 10 right parenthesis end fraction hours.

[3]
ii)
Find the difference between the time taken for each of the two journeys when x space equals space 80.
Give your answer in minutes and seconds.
 
................... min .................. s  [3]

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3
Sme Calculator3 marks

straight f open parentheses x close parentheses equals 8 minus 3 x  and  straight g left parenthesis x right parenthesis equals fraction numerator 10 over denominator x plus 1 end fraction comma space x not equal to negative 1.


Write straight f left parenthesis x right parenthesis plus straight g left parenthesis x right parenthesis as a single fraction in its simplest form.

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4
Sme Calculator4 marks

2 minus fraction numerator x plus 2 over denominator x minus 3 end fraction minus fraction numerator x minus 6 over denominator x plus 3 end fraction can be written as a single fraction in the form  fraction numerator a x plus b over denominator x squared minus 9 end fraction where a and b are integers.

Work out the value of a and the value of b.

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5
Sme Calculator3 marks

Show that  fraction numerator 1 over denominator 6 x squared plus 7 x minus 5 end fraction divided by fraction numerator 1 over denominator 4 x squared minus 1 end fraction  simplifies to  fraction numerator a x plus b over denominator c x plus d end fraction where a, b, c and d are integers.

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