Final answer:
Combining like terms, we obtain an equation with z, which we can solve by simplifying and dividing both sides by a constant, will get z = 1.59.
Step-by-step explanation:
To solve the equation 3 1/5 / (z-1/2) = 2 2/3 / (z+1/3), we can simplify both sides by finding a common denominator. The common denominator for (z-1/2) and (z+1/3) is 6, so the equation becomes:
19 / 6(z-1/2) = 8 /3(z+1/3)
To eliminate the denominators, we can multiply both sides of the equation by 6. This gives us:
19(z-1/2) = 8(z+1/3)
Expanding both sides, we get:
19z - 9.5 = 8z + 8/3
Combining like terms, we have:
19z - 8z = 9.5 + 8/3
11z = 9.5 + 8/3
To solve for z, we can first simplify the right side of the equation:
11z = 9.5 + 24/3
11z = 9.5 + 8
11z = 17.5
Finally, dividing both sides of the equation by 11, we find that z = 17.5 / 11 = 1.59.