chefo's HW 2

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Q15

$$\begin{array}{r}\\ f(x)=& \frac{2}{4p-20}+\frac{p-6}{p^2-8p+15}\\ f(x)=& \frac{2}{4(p-5)}+\frac{p-6}{(p-5)(p-3)}\end{array}$$

Multiply both the numerator and denominator of the first fraction by

$(p-3)$, and multiply both the numerator and denominator of the second fraction by

$4$.

$$\begin{array}{c}\\ f(x)=& \frac{2(p-3)}{4(p-5)(p-3)}+\frac{4(p-6)}{4(p-5)(p-3)}\end{array}$$

Now the denominator is the same, so we can combine the numerator now.

$$\begin{array}{cc}f(x)=& \frac{2(p-3)+4(p-6)}{4(p-5)(p-3)}\end{array}$$

I don't think I need to continue. OK, I was wrong.

$$\begin{array}{cc}f(x)=& \frac{2p-6+4p-24}{4(p-5)(p-3)}\\ f(x)=& \frac{6p-30}{4(p-5)(p-3)}\\ f(x)=& \frac{6(p-5)}{4(p-5)(p-3)}\end{array}$$

At here, we can cancel that

$(p-5)$.

$$\begin{array}{cc}f(x)=& \frac{6}{4(p-3)}\\ f(x)=& \frac{3}{2(p-3)}\\ f(x)=& \frac{3}{2p-6}\end{array}$$