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Show that \[ \frac{4x + 3}{2x} + \frac{3}{5} \] can be written in the form \[ \frac{ax + h}{cx} \] where a, b and c are integers. - Edexcel - GCSE Maths - Question 16 - 2021 - Paper 1

Question 16

$Show-that---\[-\frac{4x-+-3}{2x}-+-\frac{3}{5}-\]---can-be-written-in-the-form---\[-\frac{ax-+-h}{cx}-\]---where-a,-b-and-c-are-integers.-Edexcel-GCSE Maths-Question 16-2021-Paper 1.png$

Show that \[ \frac{4x + 3}{2x} + \frac{3}{5} \] can be written in the form \[ \frac{ax + h}{cx} \] where a, b and c are integers.

Worked Solution & Example Answer:Show that \[ \frac{4x + 3}{2x} + \frac{3}{5} \] can be written in the form \[ \frac{ax + h}{cx} \] where a, b and c are integers. - Edexcel - GCSE Maths - Question 16 - 2021 - Paper 1

Step 1

Write each fraction with a common denominator

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Answer

To combine the fractions, we need a common denominator. The two denominators are (2x) and (5). The least common multiple is (10x). Thus, we rewrite the fractions:

[ \frac{4x + 3}{2x} = \frac{5(4x + 3)}{10x} = \frac{20x + 15}{10x} ]
[ \frac{3}{5} = \frac{2(3)}{10} = \frac{6}{10} ]

Now, adding the two fractions together gives:

[ \frac{20x + 15}{10x} + \frac{6}{10} = \frac{20x + 15 + 6}{10x} = \frac{20x + 21}{10x} ]

Step 2

Combine the numerators

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Answer

Thus, we can express the sum as:

[ \frac{20x + 21}{10x} ]

which is in the form ( \frac{ax + h}{cx} ) where ( a = 20 ), ( h = 21 ), and ( c = 10 ). The values for (a), (b), and (c) are integers.

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