Subtract. Simplify, if possible. d/y+d - d/y-d?

Question

Subtract. Simplify, if possible

d/y+d - d/y-d=

Answer 1

You need a common denominator to subtract these fractions.  Use (y + d)(y - d) as the common denominator and multiply the first fraction by (y - d) / (y - d) and the second fraction by (y + d) / (y + d).

[d/(y + d)] - [d/(y - d)] =

[(y - d)/(y - d)][d/(y + d)] - [d/(y - d)][(y + d)/(y + d)] =

[(y - d)/(y - d)][d/(y + d)] - [d/(y - d)][(y + d)/(y + d)] =

[d(y - d)]/[(y + d)(y - d)] - [d(y + d)]/[(y + d)(y - d)] =

[d(y - d) - d(y + d)]/[(y + d)(y - d)] =

[d(y - d - y - d)]/[(y + d)(y - d)] =

[d(-2d)]/[(y + d)(y - d)] =

(-2d²)/((y + d)(y - d))

Hope this helps you!