Simplify
$$\frac{7 + \sqrt{5}}{\sqrt{5} - 1}$$
giving your answer in the form $a + \frac{b}{\sqrt{5}}$, where $a$ and $b$ are integers. - Edexcel - A-Level Maths Pure - Question 3 - 2013 - Paper 1
Question 3
Simplify
$$\frac{7 + \sqrt{5}}{\sqrt{5} - 1}$$
giving your answer in the form $a + \frac{b}{\sqrt{5}}$, where $a$ and $b$ are integers.
Worked Solution & Example Answer:Simplify
$$\frac{7 + \sqrt{5}}{\sqrt{5} - 1}$$
giving your answer in the form $a + \frac{b}{\sqrt{5}}$, where $a$ and $b$ are integers. - Edexcel - A-Level Maths Pure - Question 3 - 2013 - Paper 1
Step 1
Step 1: Multiply the Numerator and Denominator
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Answer
To simplify the expression, we will multiply both the numerator and the denominator by the conjugate of the denominator, which is 5+1.
(5−1)(5+1)(7+5)(5+1)
Step 2
Step 2: Simplify the Denominator
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Answer
Calculating the denominator:
(5)2−(1)2=5−1=4
Step 3
Step 3: Expand the Numerator
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Answer
Now, expanding the numerator:
(7+5)(5+1)=75+7+5+5=7+5+85=12+85
Step 4
Step 4: Combine the Results
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