1 of 8 0-day streak

Simplify and combine algebraic fractions

Question 1 of 8

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Consider the algebraic fraction expression \(\frac{x^{2} - 25}{x - 6}\cdot\frac{-2x - 2}{x^{3} + 6x^{2} - 25x - 150}\)

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 correct first setup for the stated algebraic fraction expression

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

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

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

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

(b)1 mark

Choose the result with the correct factor cancellation and domain restrictions

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

\frac{-2x - 2}{x^{2} - 35}\quad x\ne -6,\ x\ne -5,\ x\ne 5,\ x\ne 6

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

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

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

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