Question

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Answer 1

\(a,\dfrac{a+b}{a+b+c}+\dfrac{b+c}{a+b+c}+\dfrac{c+a}{a+b+c}=\dfrac{a+b+b+c+c+a}{a+b+c}=\dfrac{2a+2b+2c}{a+b+c}=\dfrac{2\left(a+b+c\right)}{a+b+c}=2\)

\(b,\dfrac{6x-3}{x}:\dfrac{4x^2-1}{3x^2}=\dfrac{3x^2.3\left(2x-1\right)}{x\left(4x^2-1\right)}=\dfrac{9x\left(2x-1\right)}{\left(2x-1\right)\left(2x+1\right)}=\dfrac{9x}{2x+1}\)

Answer 2

a)

\(=\dfrac{2\left(a+b+c\right)}{a+b+c}=2\)

b) \(=\dfrac{3\left(2x-1\right)}{x}.\dfrac{3x^2}{\left(2x-1\right)\left(2x+1\right)}=\dfrac{9x}{2x+1}\)