How do you add or subtract #(x+6)/(5x+10) - (x-2)/(4x+8)#?

Answer 1
Notice that the denominator of each of these terms is a simple multiple of #(x+2)#, so we only need to multiply by constants to make the denominators of the two terms the same:
#(x+6)/(5x+10)-(x-2)/(4x+8)#
#=(x+6)/(5(x+2))-(x-2)/(4(x+2))#
#=(4*(x+6))/(4*5(x+2))-(5*(x-2))/(5*4(x+2))#
#=(4(x+6))/(20(x+2))-(5(x-2))/(20(x+2))#
#=(4(x+6)-5(x-2))/(20(x+2))#
#=(4x+24-5x+10)/(20(x+2))#
#=(14-x)/(20(x+2))#
#=(14-x)/(20x+40)#
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Answer 2

To add or subtract fractions, you need a common denominator. In this case, the common denominator is (5x+10)(4x+8).

To subtract the fractions, you need to distribute the negative sign to the second fraction.

The expression becomes:

[(x+6)/(5x+10)] - [(x-2)/(4x+8)]

To find the numerator of the result, you need to multiply each fraction by the common denominator.

The expression becomes:

[(x+6)(4x+8)]/[(5x+10)(4x+8)] - [(x-2)(5x+10)]/[(4x+8)(5x+10)]

Simplify the numerators:

[(4x^2 + 20x + 8x + 48)]/[(5x+10)(4x+8)] - [(5x^2 - 10x + 10x - 20)]/[(4x+8)(5x+10)]

Combine like terms:

[(4x^2 + 28x + 48)]/[(5x+10)(4x+8)] - [(5x^2 - 20)]/[(4x+8)(5x+10)]

Now, subtract the fractions by subtracting the numerators:

[(4x^2 + 28x + 48) - (5x^2 - 20)]/[(5x+10)(4x+8)]

Simplify the numerator:

[4x^2 + 28x + 48 - 5x^2 + 20]/[(5x+10)(4x+8)]

Combine like terms:

[-x^2 + 28x + 68]/[(5x+10)(4x+8)]

The final result is:

(-x^2 + 28x + 68)/[(5x+10)(4x+8)]

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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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