Simplify (qx+a)/(rx+b) +/- (sx+c)/(tx+d)
\nx is a randomised variable. a,b,c,d,q,r,s,t are randomised integers. a,b,c,d run from -5 to 5, including 0. q,r,s,t run from -3 to 3, and can be 0 if the constant term is nonzero, but are mostly 1.
", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "Express $\\displaystyle{\\var{te[0]}\\var{sgnl}\\var{te[1]}}$ as a single fraction.
", "advice": "\\[\\begin{align*} \\var{te[0]}\\var{sgnl}\\var{te[1]} &= \\frac{\\var{ndnde[3]}}{\\var{ndnde[3]}}\\times\\var{te[0]}\\var{sgnl}\\frac{\\var{ndnde[1]}}{\\var{ndnde[1]}}\\times\\var{te[1]}\\\\&=\\frac{\\var{cnd[0]}\\var{sgnl}\\var{cnd[1]}}{(\\var{ndnde[1]})(\\var{ndnde[3]})}\\\\&=\\frac{(\\var{cnd[2]})\\var{sgnl}(\\var{cnd[3]})}{(\\var{ndnde[1]})(\\var{ndnde[3]})}\\\\&=\\frac{\\var{cnd[4]}}{(\\var{ndnde[1]})(\\var{ndnde[3]})}\\\\&=\\var{ans} \\end{align*}\\]
\nThere is no benefit in expanding the denominator. In fact, it is best to leave the denominator factorised, because then it is easier to see if the fraction can be simplified.
\nThe next step after this would be to try to factorise the numerator, and then see if the fraction can be simplified.
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\n0) numerator term 1, 1) numerator term 2,
\n2) brackets expanded num t1, 3) brackets expanded num t2
\n4) numerator, no brackets
\n5) numerator simplified
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