Final answer:
To add the fractions (-7)/(6v²) and (5)/(3v³), first find a common denominator by multiplying the second fraction by 2v/2v, combining the fractions, and then simplifying the result to (10v - 7)/(6v³).
Step-by-step explanation:
To add the two fractions (-7)/(6v²) and (5)/(3v³), we need to find a common denominator. Since the denominators have v raised to different powers, we'll manipulate them to make the bases and exponents match. First, observe that the least common multiple (LCM) of 6 and 3 is 6, and we want the v terms to have the same exponent. To do this, we can multiply the second fraction by 2v/2v, as this will not change its value but will match the exponent in the denominator of the first fraction. Thus, we have:
(-7)/(6v²) + (5)/(3v³) × (2v)/(2v) = (-7)/(6v²) + (10v)/(6v³)
Now, since both denominators are the same, we can combine the numerators:
(-7 + 10v)/(6v³) = (10v - 7)/(6v³)