1 of 8 0-day streak

Simplify and combine algebraic fractions

Question 1 of 8

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Consider the algebraic fraction expression \(\frac{x^{2} - 16}{2x^{2} + 4x - 16}\)

The variable is real. Values that make an original denominator zero are excluded; for division, the divisor must also be non-zero

Use exact factorisation, operation and domain information

(a)1 mark

Select the factorised setup for the stated operation

\frac{(x-4)(x+4)}{2(x+4)(x-2)}\quad x\ne 2

\frac{(x-4)(x+4)}{2(x+4)(x-2)}\quad x\ne -4,\ x\ne 2

\frac{(x-4)(x+4)}{3(x+4)(x-2)}\quad x\ne -4,\ x\ne 2

\frac{2(x-4)(x+4)}{2(x+4)(x-2)}\quad x\ne -4,\ x\ne 2

(b)1 mark

Select the fully simplified result of the stated expression

\frac{\frac{1}{2}(x-4)}{(x-2)}\quad x\ne -4,\ x\ne 2

\frac{\frac{1}{2}x - 1}{(x-2)}\quad x\ne -4,\ x\ne 2

\frac{\frac{1}{2}(x-4)}{(x-2)}\quad x\ne 2

\frac{\frac{1}{2}x - 2}{x - 1}\quad x\ne -4,\ x\ne 2

At \(x=6\), complete the exact check using the numerator, denominator and value of the simplified result

\(D(6)\) \(N(6)\) \(\frac{N(6)}{D(6)}\)