Answer:
[tex]\frac{x^{2} + 19x + 102}{4(x + 5)(x + 7)}[/tex]
Step-by-step explanation:
I have factored and multiplied lwh to get the volumes
Vol. = [tex]\frac{2x - 1}{(2x - 3)(x + 5)}[/tex] [tex]\frac{2(2x - 3)}{3x - 1}[/tex][tex]\frac{(3x - 1)(x + 3)}{(2x - 1)(x + 3)}[/tex] + [tex]\frac{x - 5}{3x + 2}[/tex][tex]\frac{3x + 2}{4}[/tex][tex]\frac{x - 2}{(x + 7)(x - 5)}[/tex]
= [tex]\frac{4}{x + 5}[/tex] + [tex]\frac{x - 2}{4(x + 7)}[/tex]
= [tex]\frac{4(4)(x + 7) + (x - 2)(x + 5)}{4(x + 5)(x + 7)}[/tex]
= [tex]\frac{16x + 112 + x^{2} + 3x -10}{4(x + 5)(x + 7)}[/tex]
= [tex]\frac{x^{2} + 19x + 102}{4(x + 5)(x + 7)}[/tex]
If I have done everything correctly, then [tex]\frac{x^{2} + 19x + 102}{4(x + 5)(x + 7)}[/tex] is the total volume
This a real exercise in factoring and multiplying and adding fractions
