[tex]f(x)=\dfrac{5x+7}{7x-5},\ g(x)=\dfrac{8x}{7x-5}\\\\(f+g)(x)=f(x)+g(x)=\dfrac{5x+7}{7x-5}+\dfrac{8x}{7x-5}=\dfrac{5x+7+8x}{7x-5}=\dfrac{13x+7}{7x-5}\\\\(f-g)(x)=f(x)-g(x)=\dfrac{5x+7}{7x-5}-\dfrac{8x}{7x-5}=\dfrac{5x+7-8x}{7x-5}=\dfrac{-3x+7}{7x-5}\\\\(f\cdot g)(x)=f(x)\cdot g(x)=\dfrac{5x+7}{7x-5}\cdot\dfrac{8x}{7x-5}=\dfrac{(5x+7)(8x)}{(7x-5)(7x-5)}\\\\=\dfrac{40x^2+56x}{(7x)(7x)+(7x)(-5)+(-5)(7x)+(-5)(-5)}=\dfrac{40x^2+56x}{49x^2-70x+25}[/tex]
