Complex fractions can be challenging to simplify, but with a few techniques, it is possible to express them in equivalent forms. In this article, we will explore one complex fraction and demonstrate how to express it in an equivalent form.
The complex fraction we will consider is:
(2x + 5)/(3x – 1) / (4x + 7)/(5x + 2)
To simplify this complex fraction, we can use the following steps:
Step 1: Flip the second fraction in the numerator and denominator
(2x + 5)/(3x – 1) * (5x + 2)/(4x + 7)
Step 2: Simplify each fraction in the numerator and denominator
(10x^2 + 29x + 10)/(12x^2 + 29x – 7)
Now, we have expressed the complex fraction in an equivalent form. We can check that it is equivalent by multiplying out the original expression and the simplified expression and comparing the results.
(2x + 5)/(3x – 1) / (4x + 7)/(5x + 2) = (2x + 5)/(3x – 1) * (5x + 2)/(4x + 7)
= (10x^2 + 29x + 10)/(12x^2 + 29x – 7)
Therefore, we have shown that the simplified expression is equivalent to the original complex fraction. This equivalent form may be useful for further algebraic manipulations or to gain a better understanding of the underlying structure of the expression.
In summary, complex fractions can be simplified by flipping and simplifying the fractions in the numerator and denominator. By following these steps, we have expressed a complex fraction in an equivalent form, which can be helpful for further calculations or understanding.