a, (\(\frac{x+1}{x-1}-\frac{x-1}{x+1}\)) : \(\frac{2x}{5x-5}\) ⇌ ( \(\frac{\left(x-1\right)\left(x+1\right)-\left(x+1\right)\left(x-1\right)}{\left(x-1\right)\left(x+1\right)}\)) . \(\frac{5\left(x-1\right)}{2x}\) ⇌ \(\frac{5\left(x-1\right)}{2x}\)
b, Khi x = 3 ta có : A = \(\frac{5\left(X-1\right)}{2X}\) = \(\frac{5\left(3-1\right)}{2.3}\)= \(\frac{10}{6}\)
Khi x = -1 ta có : A = \(\frac{5\left(-1-1\right)}{2.\left(-1\right)}\)= \(\frac{-10}{-2}\)= 5
c, 2 = \(\frac{5\left(x-1\right)}{2x}\)⇌ 2x = 5(x-1) ⇌ 2x = 5x -5 ⇌ 5 = 3x ⇌ x = \(\frac{5}{3}\)
Để A = 2 thì x = \(\frac{5}{3}\)
a, Rút gọn A
A= (\(\frac{x+1}{x-1}-\frac{x-1}{x+1}\)): \(\frac{2x}{5x-5}\)
=\(\frac{\left(x+1\right)^2-\left(x-1\right)^2}{\left(x-1\right)\left(x+1\right)}.\frac{5\left(x-1\right)}{2x}\)
=\(\frac{x^2+2x+1-x^2+2x-1}{\left(x-1\right)\left(x+1\right)}.\frac{5\left(x-1\right)}{2x}\)
=\(\frac{4x}{\left(x-1\right)\left(x+1\right)}.\frac{5\left(x-1\right)}{2x}\)
=\(\frac{10}{x+1}\)
b, tìm giá trị của A tại x=3; x=-1
x=3 => A=\(\frac{10}{4}=\frac{5}{2}\)
x=-1 => A= 0
c, tìm x để A=2
A=2 => \(\frac{10}{x+1}=2\) <=> 2x+2=10
<=> 2x=8 <=> x=4
thấy bài này cx dễ mà bạn ?
