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Multiplying fractions can seem a bit tricky at first, but it's quite simple once you get the hang of it. When multiplying fractions, you multiply the top numbers (numerators) together and the bottom numbers (denominators) together.
For example, let's consider the fractions \(-\frac{9}{7}\) and \(-\frac{7}{9}\):
\(-\frac{9}{7} \cdot -\frac{7}{9} = \frac{9 \cdot 7}{7 \cdot 9} = \frac{63}{63} = 1\).
Note how both negative signs cancel each other out, resulting in a positive number. The final answer turns out to be 1, making the multiplication straightforward.

Understanding numerators and denominators is key in simplifying algebraic expressions involving fractions. The numerator is the top part of a fraction and indicates how many parts we have. The denominator is the bottom part and indicates into how many parts the whole is divided.
For the fraction \(-\frac{9}{7}\), \-9 is the numerator, and 7 is the denominator. Likewise, for the fraction \(-\frac{7}{9}\), \-7 is the numerator and 9 is the denominator.
During multiplication, both numerators and denominators are multiplied separately. In our example: \(-\frac{9}{7} \cdot -\frac{7}{9} = \frac{9 \cdot 7}{7 \cdot 9} = \frac{63}{63} = 1\).
Each step confirms how numerators and denominators interact to simplify the fraction.

Variable coefficients are the numerical values that multiply variables in algebraic expressions. For instance, in the original problem, \(-\frac{9}{7}\) and \(-\frac{7}{9}\) are coefficients multiplying the variable x.
When simplifying, we first deal with the coefficients and then apply the result to the variable. Here, \(-\frac{9}{7} \cdot -\frac{7}{9} = 1\).
Thus, the simplified expression becomes \1 \cdot x = x\. This shows that the variable remains unaffected by the multiplication of its coefficients, simplifying the expression effectively.