How do you solve #(6x)/(x+4)+4=(2x+2)/(x1)#?
The solution for this equation is
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To solve the equation (6x)/(x+4)+4=(2x+2)/(x1), you can follow these steps:

Start by multiplying both sides of the equation by the denominators (x+4) and (x1) to eliminate the fractions.

Simplify the equation by distributing and combining like terms.

Rearrange the equation to isolate the variable on one side.

Solve for x by applying the appropriate algebraic operations.
The solution to the equation will be the value(s) of x that satisfy the equation after simplification and solving.
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To solve the equation (6x)/(x+4) + 4 = (2x+2)/(x1), follow these steps:
 Find a common denominator for both fractions.
 Multiply both sides of the equation by the common denominator to clear the fractions.
 Simplify and solve the resulting equation.
 Check for any extraneous solutions.
Here's a stepbystep breakdown:

The common denominator for the fractions is (x+4)(x1).

Multiply both sides of the equation by (x+4)(x1) to clear the fractions:
(x+4)(x1) * [(6x)/(x+4) + 4] = (x+4)(x1) * [(2x+2)/(x1)]

Simplify:
6x(x1) + 4(x+4)(x1) = (2x+2)(x+4)

Expand and simplify each side:
6x^2  6x + 4(x^2 + 3x  4) = 2x^2 + 10x + 8
6x^2  6x + 4x^2 + 12x  16 = 2x^2 + 10x + 8
10x^2 + 6x  16 = 2x^2 + 10x + 8
10x^2  2x^2 + 6x  10x  16  8 = 0
8x^2  4x  24 = 0

Factor or use the quadratic formula to solve for x.

After solving for x, check the solutions to ensure they are valid for the original equation.
That's the method to solve the given equation.
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When evaluating a onesided 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 onesided 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 onesided 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 onesided 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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