a)

\(P=\dfrac{x^{10}-x^8+x^6-x^4+x^2-1}{x^4-1}\)

\(=\dfrac{x^8\left(x^2-1\right)+x^4\left(x^2-1\right)+\left(x^2-1\right)}{\left(x^2-1\right)\left(x^2+1\right)}\)

\(=\dfrac{\left(x^2-1\right)\left(x^8+x^4+1\right)}{\left(x^2-1\right)\left(x^2+1\right)}\)

\(=\dfrac{x^8+x^4+1}{x^2+1}\)

b)

\(Q=\dfrac{x^{40}+x^{30}+x^{20}+x^{10}+1}{x^{45}+x^{40}+x^{35}+...+x^{10}+x^5+1}\)

\(=\dfrac{x^{40}+x^{30}+x^{20}+x^{10}+1}{\left(x^{45}+x^{35}+...+x^5\right)+\left(x^{40}+x^{30}+...+1\right)}\)

\(=\dfrac{x^{40}+x^{30}+x^{20}+x^{10}+1}{x^5\left(x^{40}+x^{30}+...+1\right)+\left(x^{40}+x^{30}+...+1\right)}\)

\(=\dfrac{x^{40}+x^{30}+x^{20}+x^{10}+1}{\left(x^{40}+x^{30}+...+1\right)\left(x^5+1\right)}\)

\(=\dfrac{1}{\left(x^5+1\right)}\)

Đặt biểu thức là A, ta có:

\(A=\frac{x^{40}+x^{30}+x^{20}+x^{10}+1}{x^{45}+x^{40}+x^{35}+...+x^{10}+x^5+1}\)

\(\Rightarrow A.x^5=\frac{x^{45}+x^{35}+x^{25}+x^{15}+x^5}{x^{45}+x^{40}+x^{35}+...+x^{10}+x^5+1}\)

\(\Rightarrow A.x^5+A=\frac{x^{45}+x^{40}+x^{35}+x^{25}+x^{15}+x^5+x^{40}+x^{30}+x^{20}+x^{10}+1}{x^{45}+x^{40}+x^{35}+...+x^{10}+x^5+1}\)

\(\Rightarrow A.x^5+1=1\)

\(\Rightarrow A=\frac{1}{x^5+1}\)

\(\left(27.700-45.20\right)\div\left(45-40+35-30+25-20+15-10+5\right)\)

\(=\)\(\left(27.100-45.20\right)\div25\)

\(=\)\(\left(27.35.20-45.20\right)\div25\)

\(=\)\(\left[\left(27.35-45\right).20\right]\div25\)

\(=\)\(18000\div25\)

\(=\)\(750\)

Hướng dẫn giải:

a) 3 x (20 – 5)

Cách 1:

3 x (20 – 5) = 3 x 15 = 45

Cách 2:

3 x (20 – 5) = 3 x 20 – 3 x 5 = 60 – 15 = 45

b) 20 x (40 – 1)

Cách 1:

20 x (40 – 1) = 20 x 39 = 780

Cách 2:

20 x (40 – 1) = 20 x 40 – 20 x 1 = 800 – 20 = 780

\(\dfrac{3x-40}{50}+\dfrac{3x-10+2x+60+4x-360}{40}=0\)

=> \(\dfrac{3x-40}{50}+\dfrac{9x-310}{40}=0\)

=> \(\dfrac{3x-40}{50}=\dfrac{-9x+310}{40}\)

=> \(40\left(3x-40\right)=50\left(-9x+310\right)\)

=> \(120x-1600=-450x+15500\)

=> \(120x+450x=15500+1600\)

Hay \(570x=17100\)

=>x = 30

Hơi dài nhé bạn

\(\dfrac{3x-40}{50}\)+\(\dfrac{3x-10+2x+60+4x-360}{40}\)=0

⇒\(\dfrac{3x-40}{50}\)+\(\dfrac{9x-310}{40}\)=0

⇒\(\dfrac{3x-40}{50}\)=\(\dfrac{9x-310}{40}\)

⇒40(3x -40) = 50(-9x+310)

⇒120x - 1600 = -450x + 15500

⇒120x + 450x = 15500 + 1600

Mặt khác: 570x = 17100

⇒x = 30

\(\dfrac{x-55}{45}+\dfrac{x-30}{35}+\dfrac{x-25}{25}+\dfrac{x-40}{15}=10\)

\(< =>\dfrac{x-55}{45}+\dfrac{x-30}{35}+\dfrac{x-25}{25}+\dfrac{x-40}{15}-10=0\)

\(< =>\dfrac{x-55}{45}-1+\dfrac{x-30}{35}-2+\dfrac{x-25}{25}-3+\dfrac{x-40}{15}-4=0\)

\(< =>\dfrac{x-100}{45}+\dfrac{x-100}{35}+\dfrac{x-100}{25}+\dfrac{x-100}{15}=0\)

\(< =>\left(x-100\right)\left(\dfrac{1}{45}+\dfrac{1}{35}+\dfrac{1}{25}+\dfrac{1}{15}\right)=0\)

\(< =>x-100=0\left(\dfrac{1}{45}+\dfrac{1}{35}+\dfrac{1}{25}+\dfrac{1}{15}\ne0\right)\)

\(< =>x=100\)

9: =3/2*5/12+3/16

=15/24+3/16

=5/8+3/16

=13/16