How do you solve the rational equation #(x+2)/(x+1)-(x-4)/(x-3)=0#?

Answer 1

#x=1#

add #[x-4]/[x-3]# to both sides
#[x+2]/[x+1]=[x-4]/[x-3]#
multiply both sides by #(x+1)(x-3)#
#(x-3)(x+2)=(x-4)(x+1)#
#x^2+2x-3x-6=x^2+x-4x-4#
#x^2-x-6=x^2-3x-4#
add #x^2# to both sides
#-x-6=-3x-4#
add #3x# to both sides
#2x-6=-4#

add 6 to both sides

#2x=2#

divide by 2

#x=1#
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Answer 2

To solve the rational equation (x+2)/(x+1)-(x-4)/(x-3)=0, we can start by finding a common denominator for the fractions. The common denominator is (x+1)(x-3).

Next, we can multiply each term by the common denominator to eliminate the fractions. This gives us (x+2)(x-3) - (x-4)(x+1) = 0.

Expanding and simplifying the equation, we get x^2 - x - 6 - (x^2 - 3x + 4) = 0.

Combining like terms, we have x^2 - x - 6 - x^2 + 3x - 4 = 0.

Simplifying further, we get 2x + 6 = 0.

Subtracting 6 from both sides, we have 2x = -6.

Dividing both sides by 2, we find x = -3.

Therefore, the solution to the rational equation is x = -3.

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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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