\(\left(\frac{a}{a-1}-\frac{1}{a^2-a}\right)=\frac{a^2-1}{a^2-a}=\frac{a+1}{a}\)

ở phàn a+/a thiếu số 1 nhé

\(\frac{1}{a+1}+\frac{2}{a^2-1}=\frac{a-1+2}{a^2-1}=\frac{1}{a-1}\)

=> K =\(\frac{a^2-1}{a}\) 

đkxđ: a khác +-1

b, thay vào mà tình

a/ \(K=\left(\frac{a}{a-1}-\frac{1}{a^2-a}\right):\left(\frac{1}{a+1}+\frac{2}{a^2-1}\right)\)

\(=\left(\frac{a}{a-1}-\frac{1}{a\left(a-1\right)}\right):\left(\frac{1}{a+1}+\frac{2}{\left(a-1\right)\left(a+1\right)}\right)\)

\(=\frac{a^2-1}{a\left(a-1\right)}:\frac{a-1+2}{\left(a-1\right)\left(a+1\right)}\)

\(=\frac{\left(a-1\right)\left(a+1\right)}{a\left(a-1\right)}.\frac{\left(a-1\right)\left(a+1\right)}{a-1}\)

\(=\frac{a+1}{a}.a+1\)

\(=\frac{\left(a+1\right)^2}{a}\)

b, Thay a=1/2

\(\Rightarrow\frac{\left(\frac{1}{2}+1\right)^2}{\frac{1}{2}}=\frac{\frac{9}{4}}{\frac{1}{2}}=\frac{9}{2}\)

đồ ngốc thật hợp với tên bạn

chứng minh đa thức x^3-37x+84 luôn luôn bằng 0 đi

a, \(A=\left(\frac{x}{x^2-4}+\frac{1}{x+2}-\frac{2}{x-2}\right):\left(1-\frac{x}{x+2}\right)\)

\(=\left(\frac{x}{\left(x-2\right)\left(x+2\right)}+\frac{1}{x+2}-\frac{2}{x-2}\right):\left(1-\frac{x}{x+2}\right)\)

=\(\left(\frac{x+x-2-2x-4}{\left(x-2\right)\left(x+2\right)}\right):\left(\frac{x+2-x}{x+2}\right)\)

\(=\frac{-6}{\left(x-2\right)\left(x+2\right)}.\frac{x+2}{2}\)

\(=\frac{-3}{x-2}\)

b. Thay : x=-4

=>-3/x-2=-3/(-4)-2=1/2

câu a quy đồng mẫu lên: x^2-4=(x+2)(x-2). câu b thì thay vào. câu c toán 7 tự làm

cho hinh thang ABCD(AB song song CD).duong thang song song voi day nho AB cat cac canh AD,BD,AC,,BC theo thu tu tai cac diem M,N,P,Q, chung minh MN₫PQ

a, B=[(x+3)/(x-3)+(2x^2-6)/(9-x^2)+x/(x+3)]:[(6x-12)/(2x^2-18)]

=[(x+3)/(x-3)+ -(2x^2-6)/(x^2-9)+x/(x+3)]:[(6x-12)/(2x^2-18)]

=[(x+3)/(x-3)+ -(2x^2-6)/(x-3)(x+3)+x/(x+3)]:[(6x-12)/2(x-3)(x+3)]

={[(x+3)^2-2x^2+6+x(x-3)]/(x-3)(x+3)}:[6(x-2)/2(x-3)(x+3)]

=(x^2+6x+9-2x^2+6+x^2-3x)/(x-3)(x+3): 6(x-2)/2(x-3)(x+3)

=3x+15/(x-3)(x+3): 6(x-2)/2(x-3)(x+3)

=3(x+5)/(x-3)(x+3): 6(x-2)/2(x-3)(x+3

=3(x+5)/(x-3)(x+3).2(x-3)(x+3)/6(x-2)

=3(x+5).6/(x-2)

=6(x+5)/6(x-2)

=x+5/x-2

b,Ta thay : x=1

=>x+5/x-2=1+5/1-2=-6

Ta thay : x=-3

=>x+5/x-2=-3+5/-3-2=-2/5

c, Ta co : x+5/x-2=0

x+5=(x-2).0

x+5=0

x=-5

Vậy : x=-5

a=7744