Question

Enter the values for the highlighted variables to complete the steps to find the sum:

$\begin{array}{rcl}\frac{3x}{2x-6}+\frac{9}{6-2x}& =& \frac{3x}{2x-6}+\frac{9}{a(2x-6)}\\ & =& \frac{3x}{2x-6}+\frac{b}{(2x-6)}\\ & =& \frac{3x-c}{2x-6}\\ & =& \frac{d\left(x-e\right)}{f\left(x-3\right)}\\ & =& g\end{array}$

Answer 1

Find the values:

We have to find the value of of $a,b,c,d,e,f,\mathrm{and}g$.

To find the given value let us solve the given expression accordingly.

$\begin{array}{rcl}\frac{3x}{2x-6}+\frac{9}{6-2x}& =& \frac{3x}{2x-6}+\frac{9}{-1(2x-6)}\left[\mathrm{Taking}\left(-1\right)\mathrm{coomon}\mathrm{out}\mathrm{of}\mathrm{the}\mathrm{denominator}\mathrm{of}\mathrm{second}\mathrm{term}\right]\\ & =& \frac{3x}{2x-6}+\frac{-9}{(2x-6)}\left[\mathrm{Multiplying}\mathrm{both}\mathrm{numerator}\mathrm{and}\mathrm{denominator}\mathrm{of}\mathrm{second}\mathrm{term}\mathrm{by}\left(-1\right)\right]\\ & =& \frac{3x-9}{2x-6}\\ & =& \frac{3\left(x-3\right)}{2\left(x-3\right)}\\ & =& \frac{3}{2}\end{array}$

Compare this calculation with given calculation we get $a=-1,b=-9,c=9,d=3,e=3,f=2,g=\frac{3}{2}$.

Hence, the required values are $a=-1,b=-9,c=9,d=3,e=3,f=2,g=\frac{3}{2}$.