ANSWER
[tex]\frac{ {w}^{2} - 7w + 12}{ {w}^{2} + w - 20 } [/tex]
EXPLANATION
The given fraction is,
[tex] \frac{w - 3}{w + 5} [/tex]
To get an equivalent fraction, we multiply both the numerator and the denominator by the same quantity that will give us
w²+w-20
in the denominator.
This implies that,
[tex] \frac{w - 3}{w + 5} = \frac{(w - 3)(w - 4)}{(w + 5)(w - 4)} [/tex]
We multiply out the numerators and denominators using the distributive property to obtain,
[tex] \frac{w - 3}{w + 5} = \frac{ {w}^{2} - 4w - 3w + 12}{ {w}^{2} - 4w + 5w - 20 } [/tex]
This simplifies to
[tex] \frac{w - 3}{w + 5} = \frac{ {w}^{2} - 7w + 12}{ {w}^{2} + w - 20 } [/tex]
