equation help please!?

Question

(y-a)/a - (y-b)/b = ab

solve for y. Thanks if you can help

Answer 1

(y-a)/a - (y-b)/b = ab

multiply both sides by ab to cancel out the denominator;

thus;
(y-a)b-(y-b)a=a^2b^2

distribute:
by-ab-ay+ab=a^2b^2
combine like terms;

(by-ay)=a^2b^2
factor out y;
y(b-a)=a^2b^2

y=(a^2b^2)/(b-a)

Answer 2

in order to add (or subtract) fractions, the denominators have to be the same.

so multiply the first fraction by b/b and the 2nd fraction by a/a

Doing this doesnt change the value of each fraction, since a/a = 1 and anything times 1 is anything.

Answer 3

Hello
Multiply every term on both sides by the common denominator of ab and we have

b(y-a) -a(y-b) = a^2b^2

so by - ba -ay + ab = a^2b^2
Factor out y giving us (b-a)y = a^2b^2 and last divide by -a and we have

y = (a^2b^2)/(b-a)

Hope This Helps!!

Answer 4

for the first part get a common denominator, which would be ab

then you should have;

(y-a)(b)/ab - (y-b)(a)/ab = ab

now you can combine the 2 fractions:

(y-a)(b) - (y-b)(a)
---------------------- = ab
ab

multiply both sides by ab to get rid of it on the left

(y-a)(b) - (y-b)(a) = ab^2

now do the distributive property:

by - ab - ay + ab = ab^2

The two ab's will cancel out, leaving you with:

by - ay = ab^2

factor out an y

y(b-a) = ab^2

Then divide both sides by (b-a)

y = ab^2/(b-a)

Answer 5

Always try to get rid of pesky fractions first.

We can do this by multiplying everything by ab. So:
(y-a)b - (y-b)a = ab*ab
so
yb - ab - ya +ab = (ab)^2
so
y = (ab)^2 / (b-a)
.

Answer 6

Multiply all three terms by (ab). This leaves...
b(y-a) - a(y-b) = (ab)^2
Simplify...
by-ab-ay-ab = (ab)^2
Add like terms...
by-ay-2ab = (ab)^2
Add 2ab to both sides...
by-ay = (ab)^2 + 2ab
Pull out y, Y(b-a) = (ab)^2 + 2ab
Divide by (b-a)
Y = [(ab)^2 + 2ab]/ (b-a)

Answer 7

Multiply everything by ab to start
b(y-a)-a(y-b)=(ab)^2
by-ab-ay+ab=(ab)^2...simplifies to
y(b-a)=(ab)^2..now divide by (b-a)
y=[(ab)^2]/(b-a) or
y=[(a^2)(b^2)]/(b-a)

Answer 8

y-a/a - (y-b)/b = ab
multiply both sides by ab
(y-a)ab/a - (y-b)ab/b =(ab)^2 ( ^2 =square0
(y-a)b - (y-b)a =(ab)^2
yb -ab -ya +ab =(ab)^2
ab cancels
yb-ya = ab^2
y(b-a)=ab^2
y=ab^2/b-a