How do you simplify #\frac { 3y ^ { 3} - 9} { 4y ^ { 4} } - \frac { 7y ^ { 3} - 9} { 4y ^ { 4} }#?

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Answer 1 · 2017-10-13T01:05:45

#(3y^3-9)/(4y^4)-(7y^3-9)/(4y^4)=color(blue)(-1/y#

Simplify:

#(3y^3-9)/(4y^4)-(7y^3-9)/(4y^4)#

Since the denominators are the same, we simply subtract the numerators.

#((3y^3-9)-(7y^3-9))/(4y^4)#

Simplify.

#(3y^3-9-7y^3+9)/(4y^4)#

Gather like terms.

#(3y^3-7y^3-9+9)/(4y^4)#

Simplify.

#-(4y^3+0)/(4y^4)#

#-(4y^3)/(4y^4)#

Simplify #4/4# to #1#.

#-(y^3)/(y^4)#

Apply the quotient rule of exponents: #a^m/a^n=a^(m-n)#.

#-(y^(3-4))=-y^-1#

Apply the negative power rule of exponents: #a^-m=1/a^m#.

#-1/y#