Question
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
start fraction, 2, divided by, 9, x, end fraction, plus, start fraction, 1, divided by, 7, x, end fraction
9x
2
+
7x
1
Answers
Answered by
GPT 3.5
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).
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).