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\(a,-\frac{9}{12}=-\frac{9:3}{12:3}=-\frac{3}{4}\)
\(\frac{-18}{-24}=\frac{\left(-18\right):\left(-6\right)}{\left(-24\right):\left(-6\right)}=\frac{3}{4}\)
\(-\frac{35}{70}=-\frac{35:35}{70:35}=\frac{1}{2}\)
\(-\frac{9}{27}=-\frac{9:9}{27:9}=-\frac{1}{3}\)
\(b,\frac{1313}{4242}=\frac{1313:101}{4242:101}=\frac{13}{42}\)
\(\frac{-353535}{-424242}=\frac{\left(-353535\right):\left(-70707\right)}{\left(-424242\right):\left(-70707\right)}=\frac{5}{6}\)
\(c,\frac{2^3\times4^3\times5^4}{8^2\times25^3\times7}=\frac{2^3\times4^3\times25^2}{8\times8^2\times25^2\times25\times7}\) ( 4^3 = 8^2 ; 5^4 = 25^2 )
\(=\frac{1}{25\times7}=\frac{1}{175}\)
\(a.\frac{-9}{-12}=\frac{-9:3}{-12:3}=\frac{-3}{-4}.\)
\(\frac{-18}{-24}=\frac{-18:6}{-24:6}=\frac{-3}{-4}\)
\(\frac{-35}{-70}=\frac{-35:35}{-70:35}=\frac{-1}{-2}\)
\(\frac{-9}{-27}=\frac{-9:9}{-27:9}=\frac{-1}{-3}\)
b) x \(\ge-7\Leftrightarrow\)7+x|=7+x ⇔B=|7+x|−(x−8)=7+x−x+8=15
c)|x+3|+|x−4| TH1: x≤−3 <=> |x+3|+|x−4|=−x−3+4−x=1−2x
TH2: −3<x≤4 <=> |x+3|+|x−4|=x+3+4−x=7
TH3: x > 4 <=>|x+3|+|x−4|=x+3+x-4=2x-1
\(A=x+\left\{\left(x+5\right)-\left[\left(5-x\right)-\left(-x-3\right)\right]\right\}\)
\(=x+\left\{\left(x+5\right)-\left[5-x+x+3\right]\right\}\)
\(=x+\left\{\left(x+5\right)-\left(5+3\right)\right\}\)
\(=x+\left\{\left(x+5\right)-8\right\}\)
\(=x+\left\{x+5-8\right\}=x+\left\{x-3\right\}\)
\(=x+x-3=2x-3\)
\(B=x.\left\{\left[-x-2-\left[x+\left(3-x\right)-\left(x+3\right)\right]\right]\right\}\)
\(=x.\left\{\left[-x-2-\left[x+3x-x-x-3\right]\right]\right\}\)
\(=x\left\{\left[-x-2-\left(4x-2x-3\right)\right]\right\}\)
\(=x\left\{\left[-x-2-\left(2x-3\right)\right]\right\}\)
\(=x\left\{-x-2-2x+3\right\}\)
\(=x\left(1-3x\right)=x-3x^2\)
\(=5^6\cdot3^5\cdot a^4\cdot b^3\cdot3^7\cdot3a\cdot b^6=5^6\cdot3^9\cdot a^5b^9\)