Question

[nguyễn thị tiêu nương]

cho a/b = c/d . tính \(\frac{a.b}{c.d}+\left[\left(\frac{a+b}{c+d}\right)^2:\left(\frac{a^2+b^2}{c^2+d^2}\right)\right]-\frac{a^2-b^2}{c^2-d^2}\)

Answer 1

[Hồ Thu Giang]

Có: \(\frac{a}{b}=\frac{c}{d}\Rightarrow\frac{a}{c}=\frac{b}{d}=\frac{a+b}{c+d}\)

=> \(\frac{a^2}{b^2}=\frac{c^2}{d^2}=\left(\frac{a+b}{c+d}\right)^2=\frac{ab}{cd}=\frac{a^2+b^2}{c^2+d^2}=\frac{a^2-b^2}{c^2-d^2}\)

=> \(\frac{ab}{cd}+\left[\left(\frac{a+b}{c+d}\right)^2:\left(\frac{a^2+b^2}{c^2+d^2}\right)\right]-\frac{a^2-b^2}{c^2-d^2}\)

= \(\frac{ab}{cd}+1-\frac{a^2-b^2}{c^2-d^2}\)

= \(1\)