Given the expression :
[tex]\frac{3x^2+2x-21}{-2x^2-2x+12}\cdot\frac{2x^2+25x+63}{6x^2+7x-49}[/tex]
so, at first , we need to factor each function of the expression :
[tex]\begin{gathered} 3x^2+2x-21=(3x-7)(x+3) \\ -2x^2-2x+12=-2(x^2+x-6)=-2(x+3)(x-2) \end{gathered}[/tex]
And for the second fraction:
[tex]\begin{gathered} 2x^2+25x+63=(2x+7)(x+9) \\ 6x^2+7x-49=(2x+7)(3x-7) \end{gathered}[/tex]
So, writing the given expression using the factors :
The result will be :
[tex]\frac{(3x-7)(x+3)}{-2(x+3)(x-2)}\cdot\frac{(2x+7)(x+9)}{(2x+7)(3x-7)}[/tex]
Cross the similar factors :
As you can see, at the numerator : (3x-7) , (x+3) and (2x+7) are similar with the same factors in the denominator
so, after crossing the similar factors, the result will be :
[tex]\frac{x+9}{-2(x-2)}=\frac{x+9}{-2x+4}[/tex]
The result is similar to :
[tex]\frac{ax+b}{cx+d}[/tex]
So, as a = 1 , the values of the other variables will be :
[tex]\begin{gathered} b=9 \\ c=-2 \\ d=4 \end{gathered}[/tex]
