Simplify $\dfrac{40 a^2 b c}{180 a c^2}$. [1] Expand $(2 x-3)(5+x)$. [2] Given that \((m+2

Question

Simplify $\dfrac{40 a^2 b c}{180 a c^2}$. [1] Expand $(2 x-3)(5+x)$. [2] Given that $(m+2 n)^2=28$ and $m^2+4 n^2=12$, find the value of $-8 m n$. [2] Simplify the following as a single fraction in its simplest form.$$ \frac{2 x}{(x-5)(x+1)}+\frac{1}{5-x} $$ [3] Part (c), source inconsistency: the stated real quantities cannot satisfy both conditions. Subtraction gives $4mn=16$, but then $(m-2n)^2=m^2+4n^2-4mn=12-16=-4$, impossible for real $m,n$. The formal calculation $-8mn=-32$ follows algebraically, but there is no real pair meeting the premise.

Accepted Answer

(a) $\frac{2ab}{9c}$ (b) $2x^2+7x-15$ (c) Formal value $-32$; the premise has no real solution (d) $\frac{x-1}{(x-5)(x+1)}$

Algebraic Expressions, Identities and Formulae - Multiplication and Division of Algebraic Fractions

Algebraic Expressions, Identities and Formulae - Multiplication and Division of Algebraic Fractions

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