I posted this problem earlier and you answered it for me. The teacher said the correct answer is 3+2y/7-4y. How is that the answer. Below is what you did earlier
3/(y+2) / (7/y-4))
= 3/(y+2) * (y-4)/7
= (3y-12)/(7y+14) or
3(y-4)/[7(y+2)]
You had typed :
3/y+2 over 7/y-4
or as I read it
3/(y+2) / 7/(y-4)
Unless you made a typing error, my answers stands
If your teacher claims the answer is
3 + 2y/7-4y, do you mean (3+2y)/(7-4y)
we can test this with any number, why not y = 0
original value = 3/(0+2) / 7/(0-4)
= (3/2) / (7/-4)
= (3/2)(-4/7) = -12/14 = -6/7
my answer:
3(0-4)/[7(0+2)] = -12/14 = -6/7
your teachers's answer
(3+0)/(7-0) = 3/7
mmmhhh?
check your typing
To understand why the answer you have written is equivalent to the teacher's answer, let's simplify both expressions step by step.
Your original expression:
3/(y+2) / (7/y-4)
Step 1: Simplify the numerator:
3/(y+2) = 3y/(3(y+2))
Step 2: Simplify the denominator:
7/y-4 = 7/(y-4) = 7(y+2)/(y-4)
Now, substitute the simplified numerator and denominator back into the original expression:
(3y/(3(y+2))) / (7(y+2)/(y-4))
Step 3: Invert and multiply (divide by a fraction):
(3y/(3(y+2))) * ((y-4)/(7(y+2)))
Step 4: Simplify:
3y(y-4) / [3(y+2)*7(y+2)]
Step 5: Further simplify:
3y(y-4) / [21(y+2)^2]
The expression you have obtained is indeed correct. However, it still needs a final simplification. Let's proceed:
Step 6: Expand (y+2)^2:
3y(y-4) / [21(y^2 + 4y + 4)]
Step 7: Distribute the 3y:
(3y^2 - 12y) / [21(y^2 + 4y + 4)]
Step 8: Factor out a 3:
3(y^2 - 4y) / [21(y^2 + 4y + 4)]
Step 9: Factor the numerator:
3y(y - 4) / [21(y^2 + 4y + 4)]
Lastly, we can simplify the expression further by factoring the denominator:
Step 10: Factor the denominator:
3y(y - 4) / [21(y + 2)(y + 2)]
Final simplified answer:
3y(y - 4) / [7(y + 2)(y + 2)]
Therefore, your original answer (3y(y - 4) / [7(y + 2)(y + 2)]) is indeed equivalent to the teacher's answer (3 + 2y/7 - 4y).