Final answer:
To simplify the expression (42(u+5))/(6(u+5)(3u+4)), cancel out the (u+5) terms in the numerator and denominator, then simplify the denominator by distributing the 6, and finally divide both the numerator and denominator by 6 to get 7/(3u+4).
Step-by-step explanation:
To simplify the expression (42(u+5))/(6(u+5)(3u+4)), we can start by canceling out the common factors in the numerator and denominator. We can cancel out the (u+5) terms in the numerator and denominator, leaving us with 42/(6(3u+4)). Next, we can simplify the denominator by distributing the 6, giving us 42/(18u+24). Finally, we can further simplify the expression by dividing both the numerator and denominator by 6, resulting in 7/(3u+4). Therefore, the simplified expression is 7/(3u+4).