a)
\(\dfrac{H}{x^2+9x+14}=\dfrac{1-x}{x+2}\)
\(\Rightarrow\dfrac{H}{x^2+7x+2x+14}=\dfrac{1-x}{x+2}\)
\(\Rightarrow\dfrac{H}{\left(x+7\right)\left(x+2\right)}=\dfrac{1-x}{x+2}\)
\(\Rightarrow\left(x+2\right)\left(x+7\right)\left(1-x\right)=H.\left(x+2\right)\)
\(\Rightarrow H=\left(x+7\right)\left(1-x\right)\)
b)
\(\dfrac{2x^2-5x+2}{x^2+5x-14}=\dfrac{2x-1}{H}\)
\(\Rightarrow\dfrac{2x^2-4x-x+2}{x^2+7x-2x-14}=\dfrac{2x-1}{H}\)
\(\Rightarrow\dfrac{\left(2x-1\right)\left(x-2\right)}{\left(x+7\right)\left(x-2\right)}=\dfrac{2x-1}{H}\)
\(\Rightarrow\left(2x-1\right)\left(x-2\right).H=\left(2x-1\right)\left(x+7\right)\left(x-2\right)\)
\(\Rightarrow H=x+7\)
