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Simplify fully \[ \frac{3x^2 - 8x - 3}{2x^2 - 6x} \] - Edexcel - GCSE Maths - Question 17 - 2018 - Paper 1
Question 17
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Simplify fully \[ \frac{3x^2 - 8x - 3}{2x^2 - 6x} \]
Worked Solution & Example Answer:Simplify fully \[ \frac{3x^2 - 8x - 3}{2x^2 - 6x} \] - Edexcel - GCSE Maths - Question 17 - 2018 - Paper 1
Step 1
Factor the numerator: 3x^2 - 8x - 3
Answer
To factor the quadratic expression in the numerator, we need to find two numbers that multiply to (3 \times -3 = -9) and sum to -8. These numbers are -9 and 1. Thus, we can rewrite the expression as:
[ 3x^2 - 9x + x - 3 = 3x(x - 3) + 1(x - 3) = (3x + 1)(x - 3) ]
Step 2
Step 3
Combine and simplify the expression
Answer
Now, substituting the factored forms back into the expression, we get:
[ \frac{(3x + 1)(x - 3)}{2x(x - 3)} ]
We can cancel the common factor of ((x - 3)) from the numerator and denominator (assuming (x \neq 3)). Thus, the simplified expression becomes:
[ \frac{3x + 1}{2x} ]