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What are the excluded values for #y=(2x+5)/(x+5)#?

Answer 1

The only excluded value is #x=-5#.

Excluded values occur when the denominator of a fraction equals zero.

In simpler terms, excluded fractions are when #x# makes it so that the bottom of the fraction is #0#.

This is because division by zero is not possible, so the value of #x# is excluded.

To solve for the excluded variable, simply take the denominator, set it equal to #0#, then solve for #x#. That will tell you what value of #x# will make the denominator #0#.

Here's what that looks like:

#x+5=0#

#x+5color(blue)-color(blue)5=0color(blue)-color(blue)5#

#xcolor(red)cancelcolor(black)(color(black)+5color(blue)-color(blue)5)=0color(blue)-color(blue)5#

#x=0color(blue)-color(blue)5#

#x=-5#

This is the excluded value for #x#. Hope this helped!

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Answer 2

Eli Assouline

The excluded value for y=(2x+5)/(x+5) is x=-5.

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Answer 3

Nathan Axel

The excluded values for the function ( y = \frac{2x+5}{x+5} ) are the values of ( x ) that would make the denominator ( x + 5 ) equal to zero. Therefore, the excluded value is ( x = -5 ). This is because division by zero is undefined, so the function is not defined at ( x = -5 ).

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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.