// Numbas version: exam_results_page_options {"name": "Luis's copy of Solve an equation in algebraic fractions", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"ungrouped_variables": ["a", "c", "b", "d", "g", "m", "q", "p", "s", "r", "t", "an2", "an1"], "metadata": {"notes": "\n \t\t \t\t\t\t\t \t\t \t\t\t\t \n \t\t", "description": "

Solve for $x$: $\\displaystyle \\frac{px+s}{ax+b} = \\frac{qx+t}{cx+d}$ with $pc=qa$.

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Cross-multiply to get:
\\[\\simplify{({p}*x+{s})*({c} * x + {d})=({q}*x+{t})*({a} * x + {b})}\\]
Multiplying out we get \\[\\simplify{{p*c}x^2 +{p*d+c*s}x+{s*d}={q*a}x^2 +{q*b+t*a}x+{t*b}}\\] Subtracting ${\\var{a*q}}x^2$ from each side we are left with \\[\\simplify{{p*d+c*s}x+{s*d}={q*b+t*a}x+{t*b}}\\] which we solve as a linear equation: \\[\\simplify{{p*d+c*s-q*b-t*a}x={t*b-s*d}}\\] and so \\[\\simplify{x={an1}/{an2}}.\\]

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Input as a fraction or an integer, not as a decimal.

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\\[\\simplify{({p}*x+{s}) / ({a} * x + {b}) = ({q}*x+{t}) / ({c} * x + {d})}\\]

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$x=\\;$ [[0]]

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If you want help in solving the equation, click on Show steps. If you do so then you will lose 1 mark.

\n \n \n ", "steps": [{"scripts": {}, "marks": 0, "prompt": "\n

Cross-multiply to get:
\\[\\simplify{({p}*x+{s})*({c} * x + {d})=({q}*x+{t})*({a} * x + {b})}\\]
Multiplying out to get \\[\\simplify{{p*c}x^2 +{p*d+c*s}x+{s*d}={q*a}x^2 +{q*b+t*a}x+{t*b}}.\\] Subtract the $x^2$ term from each side to leave a linear equation:

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Solve this equation for $x$.

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Solve the following equation for $x$.

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

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