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a, \(\dfrac{x+2}{7x+42}\) = \(\dfrac{x+2}{7.\left(x+6\right)}\) = \(\dfrac{\left(x+2\right)\left(x-6\right)}{7\left(x-6\right)\left(x+6\right)}\) (đk \(x\ne\) \(\mp\) 6)
\(\dfrac{-13x}{x^2-36}\) = \(\dfrac{-13x}{\left(x-6\right)\left(x+6\right)}\) = \(\dfrac{-7.13.x}{7.\left(x-6\right).\left(x+6\right)}\) = \(\dfrac{-91x}{7.\left(x-6\right)\left(x+6\right)}\)
b, \(\dfrac{7}{4x+16}\) = \(\dfrac{7\left(x-4\right)}{4.\left(x+4\right).\left(x-4\right)}\) (đk \(x\ne\) \(\pm\) 4)
\(\dfrac{15}{x^2-16}\) = \(\dfrac{15.4}{\left(x-4\right)\left(x+4\right).4}\) = \(\dfrac{60}{4.\left(x-4\right).\left(x+4\right)}\)
\(\frac{\left[35\left(27^2+2.9^{11}\right)\right]}{\left[15\left(8^{16}-12.3^{19}\right)\right]}=5,2\)
a: \(2004^2-16=2000\cdot2008=4016000\)
b: \(892^2+892\cdot216+108^2=1000^2=1000000\)
c: \(36^2-52\cdot36+26^2=10^2=100\)
\(72^2+144\cdot16+16^2-12^2\)
\(=\left(72^2+144\cdot16+16^2\right)-12^2\)
\(=\left(72^2+2\cdot72\cdot16+16^2\right)-12^2\)
\(=\left(72+16\right)^2-12^2\)
\(=88^2-12^2\)
\(=\left(88+12\right)\left(88-12\right)\)
\(=100\cdot76\)
\(=7600\)
\(48^2-42^2+64-52^2\)
\(=\left(48^2-52^2\right)-\left(42^2-64\right)\)
\(=\left(48^2-52^2\right)-\left(42^2-8^2\right)\)
\(=\left(48-52\right)\left(48+52\right)-\left(42+8\right)\left(42-8\right)\)
\(=-4\cdot100-50\cdot34\)
\(=-8\cdot50-50\cdot34\)
\(=-50\cdot\left(8+34\right)\)
\(=-50\cdot42\)
\(=-2100\)
a) Ta có: