How do you combine #(6y+5)/(5y-25)-(y+2)/(y-5)#?

Answer 1

#1/y#

#(6y+5)/color(red)((5y-25)) -(y+2)/(y-5)" "larr# factorise
#=(6y+5)/color(red)(5(y-5)) -(y+2)/(y-5)" "larr# find the LCD
#=(6y +5 - 5(y+2))/(5(y-5))" "larr# make equivalent fractions
#=(6y+5-5y-10)/(5(y-5))" "larr#remove brackets
#=(y-5)/(y(y-5))" "larr# collect like terms
#=cancel((y-5))/(ycancel((y-5)))" "larr# cancel like factors
#1/y#
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Answer 2

See the entire solution process below:

To subtract these two fractions they must be over a common denominator. To create a common denominator multiply the fraction on the right by the appropriate form of #1# to not change the value of the function but to create a common denominator:
#(6y + 5)/(5y - 25) - (5/5 xx (y + 2)/(y-5)) ->#
#(6y + 5)/(5y - 25) - (5 xx (y + 2))/(5 xx (y-5)) ->#
#(6y + 5)/(5y - 25) - ((5 xx y) + (5 xx 2))/((5 xx y) - (5 xx 5)) ->#
#(6y + 5)/(5y - 25) - (5y + 10)/(5y - 25)#

We can next subtract the numerators over the common denominator:

#((6y + 5) - (5y + 10))/(5y - 25) ->#
#(6y + 5 - 5y - 10)/(5y - 25) ->#
#(6y - 5y + 5 - 10)/(5y - 25) ->#
#((6 - 5)y + (5 - 10))/(5y - 25) ->#
#(1y - 5)/(5y - 25) ->#
#(y - 5)/(5y - 25)#

We can now factor the denominator and cancel common terms:

#(y - 5)/((5 xx y) - (5 xx 5)) ->#
#(y - 5)/(5(y - 5)) ->#
#color(red)(cancel(color(black)(y - 5)))/(5color(red)(cancel(color(black)((y - 5))))) ->#
#1/5#
However, from the original expression: #(5y - 25) != 0# and #(y-5) != 0# therefore, #y != 5#
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Answer 3

To combine the expressions (6y+5)/(5y-25) and (y+2)/(y-5), we need to find a common denominator. The common denominator for these expressions is (5y-25)(y-5).

Next, we can multiply the numerator and denominator of the first expression (6y+5)/(5y-25) by (y-5), and multiply the numerator and denominator of the second expression (y+2)/(y-5) by (5y-25).

After simplifying, we can combine the numerators over the common denominator.

The simplified expression is (6y^2 - 19y - 15)/(5y^2 - 50y + 125).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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