Toán A= (2/x+2 -2/x-2)*(1 + 2/x) a)rút gọn A b) tìm x để A=-1 27/07/2021 By Harper A= (2/x+2 -2/x-2)*(1 + 2/x) a)rút gọn A b) tìm x để A=-1
a)Rút gọn A: A= (2/x+2 -2/x-2)*(1 + 2/x) = [2(x-2)/(x+2)(x-2) – 2(x+2)/(x-2)(x+2)]*(1+ 2/x) = [( 2x -4 -2x -4)/(x-2)(x+2)]*(1+2/x) = [-8/(x-2)(x+2)]*(x/x+2/x) = [-8/(x-2)(x+2)]*[(x+2)/x] = [-8(x+2)]/[x.(x-2)(x+2)] = -8/x(x-2) b)Có A=-1 ⇔ -8/x(x-2) = -1 ⇔ -1.[x(x-2)] = -8 ⇔ -x² +2x =-8 ⇔ -x² +2x +8= 0 ⇔ -x² +4x-2x +8 =0 ⇔ -x(x-4) -2(x -4)= 0 ⇔ (-x-2)(x-4)= 0 ⇔ -x-2= 0 hoặc x-4 = 0 ⇔ x= -2 hoặc x=4 Vậy A=-1 khi x∈{-2; 4} Chúc bạn học tốt ^^ Trả lời
$A=$$(\frac{2}{x+2}-$ $\frac{2}{x-2}).(1+$$\frac{2}{x})$ $A=$ ($\frac{2(x-2)-2(x+2)}{(x+2)(x-2)}.($ $\frac{x+2}{x})$ $A=$ $\frac{-8}{(x+2)(x-2)}.$ $\frac{x+2}{x}$ $A=$ $\frac{-8}{x(x-2)}$ b, Ta có: $\frac{-8}{x(x-2)}$=-1 ⇒-x(x-2)=-8 ⇒-x(x-2)+8=0 ⇒-x²+2x+8=0 ⇒-x²-2x+4x+8=0 ⇒-x(x+2)+4(x+2)=0 ⇒(x+2)(4-x)=0 Th1: x+2=0 ⇒x=-2 Th2: 4-x=0⇒x=4 Vậy x=-2, x=4 Trả lời
a)Rút gọn A:
A= (2/x+2 -2/x-2)*(1 + 2/x) = [2(x-2)/(x+2)(x-2) – 2(x+2)/(x-2)(x+2)]*(1+ 2/x)
= [( 2x -4 -2x -4)/(x-2)(x+2)]*(1+2/x)
= [-8/(x-2)(x+2)]*(x/x+2/x)
= [-8/(x-2)(x+2)]*[(x+2)/x]
= [-8(x+2)]/[x.(x-2)(x+2)]
= -8/x(x-2)
b)Có A=-1 ⇔ -8/x(x-2) = -1
⇔ -1.[x(x-2)] = -8
⇔ -x² +2x =-8
⇔ -x² +2x +8= 0
⇔ -x² +4x-2x +8 =0
⇔ -x(x-4) -2(x -4)= 0
⇔ (-x-2)(x-4)= 0
⇔ -x-2= 0 hoặc x-4 = 0
⇔ x= -2 hoặc x=4
Vậy A=-1 khi x∈{-2; 4}
Chúc bạn học tốt ^^
$A=$$(\frac{2}{x+2}-$ $\frac{2}{x-2}).(1+$$\frac{2}{x})$ $A=$ ($\frac{2(x-2)-2(x+2)}{(x+2)(x-2)}.($ $\frac{x+2}{x})$ $A=$ $\frac{-8}{(x+2)(x-2)}.$ $\frac{x+2}{x}$ $A=$ $\frac{-8}{x(x-2)}$
b, Ta có: $\frac{-8}{x(x-2)}$=-1
⇒-x(x-2)=-8
⇒-x(x-2)+8=0
⇒-x²+2x+8=0
⇒-x²-2x+4x+8=0
⇒-x(x+2)+4(x+2)=0
⇒(x+2)(4-x)=0
Th1: x+2=0 ⇒x=-2
Th2: 4-x=0⇒x=4
Vậy x=-2, x=4