1 of 8 0-day streak

Simplify and combine algebraic fractions

Question 1 of 8

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Consider the algebraic fraction expression \(\frac{-x - 5}{x^{2} - 7x + 10}\cdot\frac{-x + 5}{2x^{2} - 2x - 60}\)

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

Which option shows the valid first algebraic step?

\frac{-(x+5)}{(x-5)(x-2)}\cdot\frac{-(x-5)}{2(x+5)(x-6)}\quad x\ne 2,\ x\ne 5,\ x\ne 6

\frac{(x+5)}{(x-5)(x-2)}\cdot\frac{-(x-5)}{2(x+5)(x-6)}\quad x\ne -5,\ x\ne 2,\ x\ne 5,\ x\ne 6

\frac{-(x+5)}{2(x-5)(x-2)}\quad x\ne -5,\ x\ne 2,\ x\ne 5,\ x\ne 6

\frac{-(x+5)}{(x-5)(x-2)}\cdot\frac{-(x-5)}{2(x+5)(x-6)}\quad x\ne -5,\ x\ne 2,\ x\ne 5,\ x\ne 6

(b)1 mark

Select the exact result after multiplying the algebraic fractions

\frac{\frac{1}{2}}{(x-2)(x-6)}\quad x\ne 2,\ x\ne 5,\ x\ne 6

\frac{\frac{3}{2}}{(x-2)(x-6)}\quad x\ne -5,\ x\ne 2,\ x\ne 5,\ x\ne 6

\frac{\frac{1}{2}}{x^{2} - 8x + 13}\quad x\ne -5,\ x\ne 2,\ x\ne 5,\ x\ne 6

\frac{\frac{1}{2}}{(x-2)(x-6)}\quad x\ne -5,\ x\ne 2,\ x\ne 5,\ x\ne 6

At \(x=0\), complete the exact check using the numerator, denominator and value of the simplified result

\(N(0)\) \(D(0)\) \(\frac{N(0)}{D(0)}\)