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a) 81^11.3^17/27^10.9^15
=(9^2)^11.3^17/(3^3)^10.9^15
=3^44.3^17/3^30.3^30
=3^61/3^60
=3
b) A =( (2^12.3^5 - 2^12.3^4)/ (2^12.3^6 + 2^12.3^5) ) - ((5^10.7^3 - 5^10.7^4)/(5^9.7^3 + 5^9.2^3.7^3))
=(2^12.3^4(3-1))/2^12.3^5(3+1) - 5^10.7^3(1-7)/5^9.7^3(1+8)
=2/12- (-30/9)=1/6 + 10/3 = 7/2
a. M=-1^2+2^2-3^2+4^2-...-99^2+100^2.
M=(2-1)(2+1)+(4-3)(4+3)+...+(100-99)(100+99)
M=3+7+...+199
=>2M=3+7+...+199+3+7+...+199 (198 số)
=(3+199)+(7+195)+...+(199+3) (99 cặp)
=202.99
=19998
=>M=19998:2=9999
a) 2x^2 + 3( x-1)(x+1) - 5x(x+1)
= 2x^2 + 3( x^2 -1 ) - 5x(x+1)
= 2x^2 + 3x^2 - 3 - 5x^2 - 5x
= -5x -3
a: \(=\dfrac{4x-8+2x+4-8}{\left(x-2\right)\left(x+2\right)}=\dfrac{6x-12}{\left(x-2\right)\left(x+2\right)}=\dfrac{6}{x+2}\)
b: \(=\dfrac{-x+7x-4}{3x-2}=\dfrac{6x-4}{3x-2}=2\)
c: \(=\dfrac{x}{2x+1}-\dfrac{1}{\left(2x+1\right)\left(2x-1\right)}-\dfrac{\left(x-2\right)}{2x-1}\)
\(=\dfrac{2x^2-x-1-\left(x-2\right)\left(2x+1\right)}{\left(2x+1\right)\left(2x-1\right)}\)
\(=\dfrac{2x^2-x-1-2x^2-x+4x+2}{\left(2x+1\right)\left(2x-1\right)}\)
\(=\dfrac{2x+1}{\left(2x+1\right)\left(2x-1\right)}=\dfrac{1}{2x-1}\)
d: \(=\dfrac{5}{2x-3}+\dfrac{2}{2x+3}+\dfrac{2x-33}{4x^2-99}\)
\(=\dfrac{10x+15+4x-6+2x-33}{\left(2x-3\right)\left(2x+3\right)}=\dfrac{16x-24}{\left(2x-3\right)\left(2x+3\right)}=\dfrac{8}{2x+3}\)
\(\frac{1+2.3^6}{2^3.3^6-2^3.5^3}-\frac{1+3^6}{8\left(9^3-125\right)}-\frac{5^3}{18^3-10^3}\)
\(=\frac{1+2.3^6}{2^3\left(3^6-5^5\right)}-\frac{1+3^6}{2^3\left[\left(3^2\right)^3-5^3\right]}-\frac{5^3}{\left(2.3^2\right)^3-\left(2.5\right)^3}\)
\(=\frac{1+2.3^6}{2^3\left(3^6-5^3\right)}-\frac{1+3^6}{2^3\left(3^6-5^3\right)}-\frac{5^3}{2^3\left(3^6-5^3\right)}\)
\(=\frac{\left(1+2.3^6\right)-\left(1+3^6\right)-5^3}{2^3\left(3^6-5^2\right)}\)
\(=\frac{3^6-5^3}{2^3\left(3^6-5^3\right)}\)
\(=\frac{1}{8}\)