1/(x+3)+4/(2x+6)

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Jun 15, 2024

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Rational Expression: 1/(x+3) + 4/(2x+6)

In this article, we will discuss the rational expression 1/(x+3) + 4/(2x+6) and explore ways to simplify it.

Simplifying the Expression

To simplify the expression, we need to find a common denominator for both fractions. Let's start by factoring the denominators:

x + 3 = (x + 3)

2x + 6 = 2(x + 3)

Now, we can rewrite the original expression as:

1/(x+3) + 4/(2(x+3))

To find a common denominator, we can multiply the first fraction by 2/2, which gives us:

2/(2(x+3)) + 4/(2(x+3))

Now we can add the fractions:

(2 + 4)/(2(x+3))

=(6)/(2(x+3))

=3/(x+3)

So, the simplified expression is 3/(x+3).

Conclusion

In conclusion, we have successfully simplified the rational expression 1/(x+3) + 4/(2x+6) to 3/(x+3). This process involved finding a common denominator, rewriting the fractions, and adding them together.