\(C=\dfrac{a^2+b^2-c^2+2ab}{a+b+c}\)
\(C=\dfrac{\left(a^2+2ab+b^2\right)-c^2}{a+b+c}\)
\(C=\dfrac{\left(a+b\right)^2-c^2}{a+b+c}\)
\(C=\dfrac{\left(a+b-c\right)\left(a+b+c\right)}{a+b+c}\)
\(C=a+b-c\)
a,\(C=\dfrac{a^2+b^2-c^2+2ab}{a+b+c}=\dfrac{\left(a+b\right)^2-c^2}{a+b+c}=\dfrac{\left(a+b-c\right)\left(a+b+c\right)}{a+b+c}=a+b-c\)b, \(D=\dfrac{a^2+b^2-c^2+2ab}{a^2-b^2+c^2+2ac}=\dfrac{\left(a+b\right)^2-c^2}{\left(a+c\right)^2-b^2}=\dfrac{\left(a+b-c\right)\left(a+b+c\right)}{\left(a-b+c\right)\left(a+b+c\right)}=\dfrac{a+b-c}{a-b+c}\)
\(D=\dfrac{a^2+b^2-c^2+2ab}{a^2-b^2+c^2+2ac}\)
\(D=\dfrac{\left(a^2+2ab+b^2\right)-c^2}{\left(a^2+2ac+c^2\right)-b^2}\)
\(D=\dfrac{\left(a+b\right)^2-c^2}{\left(a+c\right)^2-b^2}\)
\(D=\dfrac{\left(a+b-c\right)\left(a+b+c\right)}{\left(a+c-b\right)\left(a+c+b\right)}\)
\(D=\dfrac{a+b-c}{a+c-b}\)
