How do you solve #10 / (2x+6) + 2 / (x+3) = 1/2#?
Using the lowest common denominator.
:)
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To solve the equation 10 / (2x+6) + 2 / (x+3) = 1/2, you can follow these steps:

Find a common denominator for the fractions on the left side of the equation. In this case, the common denominator is (2x+6)(x+3).

Multiply each term by the common denominator to eliminate the fractions. This will give you: 10(x+3) + 2(2x+6) = (1/2)(2x+6)(x+3).

Simplify both sides of the equation by distributing and combining like terms. This will result in: 10x + 30 + 4x + 12 = (x+3)(x+6).

Continue simplifying the equation by combining like terms: 14x + 42 = x^2 + 9x + 18.

Rearrange the equation to bring all terms to one side: x^2  5x  24 = 0.

Factor the quadratic equation: (x  8)(x + 3) = 0.

Set each factor equal to zero and solve for x: x  8 = 0 or x + 3 = 0.

Solve for x in each equation: x = 8 or x = 3.
Therefore, the solutions to the equation 10 / (2x+6) + 2 / (x+3) = 1/2 are x = 8 and x = 3.
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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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