How do you simplify #\frac { 7s } { s ^ { 2} + 10s + 25} - \frac { 6s - 5} { s ^ { 2} + 10s + 25}#?

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Answer 1 · 2018-03-25T02:17:22

The simplified fraction is #1/(s+5)#.

Since the denominators are the same, you can combine the fractions (don't forget the parentheses when subtracting!).

Next, factor the bottom, then cancel the terms in common.

The process will look like this:

# color(white)=(7s)/(s^2+10s+25)-(6s-5)/(s^2+10s+25) #

# =(7s-(6s-5))/(s^2+10s+25) #

# =(7s-6s+5)/(s^2+10s+25) #

# =(s+5)/(s^2+10s+25) #

# =(s+5)/(s^2+5s+5s+25) #

# =(s+5)/(color(red)s(s+5)+5s+25) #

# =(s+5)/(color(red)s(s+5)+color(blue)5(s+5)) #

# =(s+5)/((color(red)s+color(blue)5)(s+5)) #

# =color(red)cancelcolor(black)((s+5))/((color(red)s+color(blue)5)color(red)cancelcolor(black)((s+5))) #

# =1/(color(red)s+color(blue)5) #

This is the simplified fraction. Hope this helped!