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a) \(\frac{a^2m-a^2n-b^2n+b^2m}{a^2+b^2}=\frac{a^2\left(m-n\right)+b^2\left(m-n\right)}{a^2+b^2}\)
\(=\frac{\left(m-n\right)\left(a^2+b^2\right)}{a^2+b^2}=m-n\)
b) \(\frac{\left(ab+bc+cd+ad\right)abcd}{\left(c+d\right)\left(a+b\right)+\left(b-c\right)\left(a-b\right)}\)
\(=\frac{\left[b.\left(a+c\right)+d.\left(a+c\right)\right].abcd}{ac+bc+da+db+ab-b^2-ca+bc}\)
\(=\frac{\left(a+c\right)\left(d+b\right)abcd}{2bc+da+db+ab-b^2}\)
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![](https://rs.olm.vn/images/avt/0.png?1311)
Xet \(M-1=a+\frac{2a+2}{2-b}-\left(\frac{2a-b}{2+b}+1\right)+\frac{4a}{b^2-4}\)
=\(a+\left(2a+2\right)\left(\frac{1}{2-b}-\frac{1}{2+b}\right)+\frac{4a}{b^2-4}\)
=\(\frac{ab^2-4a-4ab-4b+4a}{b^2-4}\)
=\(\frac{ab^2-4ab-4b}{b^2-4}\)
den doan nay em xet rieng tu so \(ab^2-4ab-4b\)
thay b=a/a+1 vao \(\frac{a^3}{\left(a+1\right)^2}-\frac{4a^2}{a+1}-\frac{4}{a+1}\)
=\(\frac{a\left(a+2\right)\left(-3a-2\right)}{\left(a+1\right)^2}\)
xet mau so b^2-4=(a/a+1)^-4
=\(\frac{\left(a+2\right)\left(-3a-2\right)}{\left(a+1\right)^2}\)
den day thay vao la xong nha
\(P=\frac{a^2m-a^2n-b^2n+b^2m}{a^2+b^2}\)
\(=\frac{a^2\left(m-n\right)+b^2\left(m-n\right)}{a^2+b^2}\)
\(=\frac{\left(a^2+b^2\right)\left(m-n\right)}{a^2+b^2}\)
\(=m-n\)