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Algebraic fractions are fractions where the numerator, the denominator, or both contain algebraic expressions (which can include variables, numbers, or both). In simple terms, they are like normal fractions but with variables thrown into the mix. For example, in the equation \(\frac{3}{4}x + \frac{5}{9} = \frac{59}{50}\), both \(\frac{3}{4}x\) and \(\frac{5}{9}\) are algebraic fractions. Working with these requires a solid understanding of both fraction manipulation and algebraic principles. Remember: every time you see a fraction with a variable, it's an algebraic fraction.

When solving equations involving these, the goal is usually to isolate the variable term. This often involves dealing with the fractions first through operations such as addition, subtraction, multiplication, and division.

Simplifying fractions means reducing them to their simplest form so that the numerator and the denominator are as small as possible. This usually involves finding the greatest common divisor (GCD) of the numerator and the denominator and dividing both by that number.

For example, in the given solution, we start with \(\frac{1124}{1350}\). To simplify this, find the GCD (which is 2 in this case) and divide both the numerator and the denominator by that value:

• \(\frac{1124 \text{ divided by } 2}{1350 \text{ divided by } 2} = \frac{562}{675}\).
• This step ensures that the fraction is in its simplest form without changing its value.
  
  Simplifying fractions is crucial as it makes further mathematical operations easier and helps present the final answer more neatly.