Year 11 Maths - Specialist Algebra I

Literal equations

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Questions

Question 1

29325

Solve for $x$: $\dfrac{a}{{x - a}} = \dfrac{b}{{x + b}}$

Answer

$x = \dfrac{{2ab}}{{b-a}}$

Worked Solution

$$
\begin{aligned}
\frac{a}{x-a} &=\frac{b}{x+b} \\
a(x+b) &=b(x-a) \\
a x+a b &=b x-a b \\
a x-b x &=-2 a b \\
x(a-b) &=-2 a b\\
x&=-\frac{2 a b}{a-b}\\
x&=\frac{2 a b}{b-a}
\end{aligned}
$$

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