Solve an equation with reciprocals

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Question 1

Solve the following equation for $x$ .

Input your answer as a fraction or an integer as appropriate and not as a decimal.

$\simplify{{s} / ({a} * x + {b}) = {t} / ({c} * x + {d})}$

$x=\;$ interpreted as $\displaystyle{}$ Expected answer:interpreted as $\displaystyle{-\frac{ 57 }{ 14 }}$

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Rearrange the equation by cross-multiplying to get:
$\simplify{{s}*({c} * x + {d}) = {t} *({a} * x + {b})}$
Multiply out to get $\simplify{{s*c}*x+{s*d}={t*a}*x+{t*b}}.$ Now solve this linear equation.

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Advice

Rearrange the equation by cross-multiplying to get:
$\simplify{{s}*({c} * x + {d}) = {t} *({a} * x + {b})}$
Multiply out to get $\simplify{{s*c}*x+{s*d}={t*a}*x+{t*b}}.$ Now this is a linear equation which is solved in the following steps: $\simplify{{s*c-t*a}*x={t*b-s*d}}$ and then $\simplify{x={t*b-s*d}/{s*c-t*a}}.$

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Solve an equation with reciprocals

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