Combine the following fractions and express in fully reduced form.
start fraction, 2, divided by, 9, x, end fraction, plus, start fraction, 1, divided by, 7, x, end fraction
9x
2
+
7x
1
To combine these fractions, we need to find a common denominator. The common denominator here is 9x * 7x.
The first fraction can be rewritten as (2/9x) * (7x/7x) = 14x/63x^2.
The second fraction can be rewritten as (1/7x) * (9x/9x) = 9x/63x^2.
Adding the fractions together, (14x/63x^2) + (9x/63x^2) = (14x + 9x) / 63x^2 = 23x / 63x^2.
To reduce this fraction, we can simplify the numerator and denominator.
23x can be factored into 23 * x.
63x^2 can be factored into 9 * 7 * x * x.
So, the fully reduced fraction is 23x / 63x^2 = (23 * x) / (9 * 7 * x * x) = 23 / (9 * 7 * x) = 23 / (63x).
To combine the fractions and express in fully reduced form, we need to find a common denominator. In this case, the common denominator is the product of the denominators, which is \(9x \cdot 7x = 63x^2\).
We then need to convert each fraction so that they have the common denominator.
For the first fraction, \(\frac{2}{9x}\), we multiply the numerator and denominator by \(\frac{7x}{7x}\) to get \(\frac{2 \cdot 7x}{9x \cdot 7x} = \frac{14x}{63x^2}\).
For the second fraction, \(\frac{1}{7x}\), we multiply the numerator and denominator by \(\frac{9x}{9x}\) to get \(\frac{1 \cdot 9x}{7x \cdot 9x} = \frac{9x}{63x^2}\).
Now, we can add the two fractions together:
\(\frac{14x}{63x^2} + \frac{9x}{63x^2} = \frac{14x + 9x}{63x^2} = \frac{23x}{63x^2}\).
Finally, we can fully reduce the fraction by dividing both the numerator and denominator by the greatest common factor. In this case, they both have a common factor of \(x\), so we can simplify the fraction to:
\(\frac{23}{63x}\).
Therefore, the combined fraction expressed in fully reduced form is \(\frac{23}{63x}\).
To combine the fractions, we need to find a common denominator for the fractions. The common denominator will be the product of the denominators, which is 9x multiplied by 7, or 63x.
Now, we can rewrite the fractions with the common denominator:
2/(9x) becomes (2 * 7)/(9x * 7) = 14/(63x)
1/(7x) becomes (1 * 9)/(7x * 9) = 9/(63x)
So, the combined fractions are:
14/(63x) + 9/(63x)
To add these fractions, we keep the common denominator and add the numerators:
(14 + 9)/(63x) = 23/(63x)
Therefore, the combined fraction in fully reduced form is 23/(63x).