// Numbas version: finer_feedback_settings {"name": "7. Adding algebraic fractions", "metadata": {"description": "

Questions on combining and simplifying algebraic fractions

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Adding two algebraic fractions with the same variable in the numberators.

", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "

Express the following as a single fraction:

\\[\\simplify[basic,unitFactor]{{Letter}/{n}+{k}{Letter}/{m}}\\]

Simplify your answer where possible.

", "advice": "

Adding algebraic fractions is the same as adding ordinary fractions. First we need to write both fractions over the same denominator by multiplying the top and bottom of both fractions

\\[\\simplify[basic,unitFactor]{{Letter}/{n}+{k}{Letter}/{m}}=\\simplify[basic,unitFactor]{{m}{Letter}/({m}{n})+{n}{k}{Letter}/({n}{m})}\\]

Finally we add the numerators together and simplify to get

\\[\\simplify[basic,unitFactor]{{m}{Letter}/({m}{n})+{n}{k}{Letter}/({n}{m})}=\\simplify[basic,unitFactor]{({m}{Letter}+{n}{k}{Letter})/({n}{m})}=\\simplify{({m}{Letter}+{n}{k}{Letter})/({n}{m})}.\\]

simplifying pL1^a/n+kL2^bL1^c/m

", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "

Express the following as a single fraction:

\\[\\simplify[basic,unitFactor,zeroPower,unitPower]{{Frac1}+{Frac2}}\\]

Simplify your answer where possible.

", "advice": "

Adding algebraic fractions is the same as adding ordinary fractions. First we need to write both fractions over the same denominator by multiplying the top and bottom of both fractions

\\[\\simplify[basic,unitFactor,zeroPower,unitPower]{{Frac1}+{Frac2}}
=\\simplify[basic,unitFactor,zeroPower,unitPower]{({Numerator1}{Denominator2})/({Denominator1}{Denominator2})+({Numerator2}{Denominator1})/({Denominator1}{Denominator2})}\\]

Finally we add the numerators together and simplify to get

\\[\\simplify[basic,unitFactor,zeroPower,unitPower]{({Numerator1}{Denominator2})/({Denominator1}{Denominator2})+({Numerator2}{Denominator1})/({Denominator1}{Denominator2})}
=\\simplify[basic,unitFactor,zeroPower,unitPower]{({Numerator1}{Denominator2}+{Numerator2}{Denominator1})/({Denominator1}{Denominator2})}
=\\simplify{({Numerator1}{Denominator2}+{Numerator2}{Denominator1})/({Denominator1}{Denominator2})}.\\]

pL1^a/n+kL2^bL1^c/m

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Adding (ax+b)/n+(cx+d)/m", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Mash Sheffield", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4679/"}, {"name": "Andrew Neate", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21832/"}], "tags": [], "metadata": {"description": "

Adding algebraic fractions with linear expressions in the numerators

", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "

Express the following as a single fraction:

\\[\\simplify[basic,unitFactor,zeroTerm]{({a}{L}+{b})/{n}+({c}{L}+{d})/{m}}\\]

Simplify your answer where possible.

", "advice": "

Adding algebraic fractions is the same as adding ordinary fractions. First we need to write both fractions over the same denominator by multiplying the top and bottom of both fractions

\\[\\simplify[basic,unitFactor,zeroTerm]{({a}{L}+{b})/{n}+({c}{L}+{d})/{m}}=\\simplify[basic,unitFactor,zeroTerm]{{m}({a}{L}+{b})/({n}{m})+{n}({c}{L}+{d})/({n}{m})}\\]

Finally we add the numerators together and simplify to get

\\[\\simplify[basic,unitFactor,zeroTerm]{{m}({a}{L}+{b})/({n}{m})+{n}({c}{L}+{d})/({n}{m})}=\\simplify[basic,unitFactor,zeroTerm]{({m}({a}{L}+{b})+{n}({c}{L}+{d}))/({n}{m})}=\\simplify{({m}{a}{L}+{m}{b}+{n}{c}{L}+{n}{d})/({n}{m})}.\\]

(ax+b)/(mx+n)+(cx+d)/(px+q)

", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "

Express the following as a single fraction:

\\[\\simplify[basic,unitFactor,zeroTerm,zeroFactor]{({a}{L}+{b})/({m}{L}+{n})+({c}{L}+{d})/({p}{L}+{q})}\\]

Simplify your answer where possible.

", "advice": "

Adding algebraic fractions is the same as adding ordinary fractions. First we need to write both fractions over the same denominator by multiplying the top and bottom of both fractions

\\[\\simplify[basic,unitFactor,zeroTerm,zeroFactor]{({a}{L}+{b})/({m}{L}+{n})+({c}{L}+{d})/({p}{L}+{q})}=\\simplify[basic,unitFactor,zeroTerm,zeroFactor]{({p}{L}+{q})({a}{L}+{b})/(({p}{L}+{q})({m}{L}+{n}))+({m}{L}+{n})({c}{L}+{d})/(({m}{L}+{n})({p}{L}+{q}))}\\]

Finally we add the numerators together and simplify to get

\\[\\simplify[unitFactor,zeroTerm,zeroFactor]{({p}{L}+{q})({a}{L}+{b})/(({p}{L}+{q})({m}{L}+{n}))+({m}{L}+{n})({c}{L}+{d})/(({m}{L}+{n})({p}{L}+{q}))}
=\\simplify[unitFactor,zeroTerm,zeroFactor]{({a*p}{L}^2+{a*q+b*p}{L}+{b*q}+{m*c}{L}^2+{m*d+n*c}{L}+{n*d})/(({m}{L}+{n})({p}{L}+{q}))}\\]
\\[=\\simplify{({a*p}{L}^2+{a*q+b*p}{L}+{b*q}+{m*c}{L}^2+{m*d+n*c}{L}+{n*d})/({m*p}{L}^2+{m*q+n*p}{L}+{n*q})}.\\]

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