1 of 8 0-day streak

Simplify and combine algebraic fractions

Question 1 of 8

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Consider the algebraic fraction expression \(\frac{-x^{2} + 25}{x^{2} + 5x}\)

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-5)(x+5)}{(x)(x+5)}\quad x\ne 0

\frac{(x-5)(x+5)}{(x)(x+5)}\quad x\ne -5,\ x\ne 0

\frac{-(x-5)(x+5)}{2(x)(x+5)}\quad x\ne -5,\ x\ne 0

\frac{-(x-5)(x+5)}{(x)(x+5)}\quad x\ne -5,\ x\ne 0

(b)1 mark

Select the fully simplified result of the stated expression

\frac{-(x-5)}{(x)}\quad x\ne 0

\frac{-(x-5)}{(x)}\quad x\ne -5,\ x\ne 0

\frac{-x + 6}{(x)}\quad x\ne -5,\ x\ne 0

\frac{-x + 5}{x + 1}\quad x\ne -5,\ x\ne 0

At \(x=4\), complete the exact check using the numerator, denominator and value of the simplified result

\(\frac{N(4)}{D(4)}\) \(N(4)\) \(D(4)\)