Answer:
The answer is:
She used the wrong common denominator
Step-by-step explanation:
Solving the given equation
![\frac{x}{x^2-5x+6}+\frac{x}{x+3}\\\\Step 1: \frac{x}{(x-2)(x-3)}+\frac{x}{x+3}\\Step2: \frac{x}{(x-2)(x-3)}+\frac{x(x-2)}{(x-2)(x+3)}\\Step3:\frac{x(x+3)+x(x-2)(x+3)}{(x-2)(x-3)(x+3)}](https://tex.z-dn.net/?f=%5Cfrac%7Bx%7D%7Bx%5E2-5x%2B6%7D%2B%5Cfrac%7Bx%7D%7Bx%2B3%7D%5C%5C%5C%5CStep%201%3A%20%5Cfrac%7Bx%7D%7B%28x-2%29%28x-3%29%7D%2B%5Cfrac%7Bx%7D%7Bx%2B3%7D%5C%5CStep2%3A%20%5Cfrac%7Bx%7D%7B%28x-2%29%28x-3%29%7D%2B%5Cfrac%7Bx%28x-2%29%7D%7B%28x-2%29%28x%2B3%29%7D%5C%5CStep3%3A%5Cfrac%7Bx%28x%2B3%29%2Bx%28x-2%29%28x%2B3%29%7D%7B%28x-2%29%28x-3%29%28x%2B3%29%7D)
Lets consider the steps given in the question:
![Step2: \frac{x}{(x-2)(x+3)}+\frac{3(x-2)}{(x-2)(x+3)}](https://tex.z-dn.net/?f=Step2%3A%20%5Cfrac%7Bx%7D%7B%28x-2%29%28x%2B3%29%7D%2B%5Cfrac%7B3%28x-2%29%7D%7B%28x-2%29%28x%2B3%29%7D)
![Step3: \frac{x+3(x-2)}{(x-2)(x+3)}\\](https://tex.z-dn.net/?f=Step3%3A%20%5Cfrac%7Bx%2B3%28x-2%29%7D%7B%28x-2%29%28x%2B3%29%7D%5C%5C)
Lets compare both solutions:
In the original solution, the denominator of first term is (x-2)(x-3)
In the solution given in the question, the denominator of first term is (x-2)(x+3).
So the mistake she did in step 2 was that she change the sign of 3 in (x-3) from negative to positive, due to which she gets the wrong common denominator shown in Step 3.
Answer:
32/9
Step-by-step explanation:
Translating the word problem into a symbolic equation yields:
3n - 3 = 5/6
Solve this for the number (n):
Multiplying both sides of this equation by 6 clears out the fraction term:
18n - 18 = 5
Adding 18 to both sides isolates 18n: 18n = 23
Then the number is n = 23/18, and:
one more than twice this number n is 2(23/18) + 1, or:
46/18 + 18/18, or 64/18, or (reducing this result)
32/9
Answer:
c I hope this helps and have a good day
Greater number would be = 9 x 6 = 54
Smaller number would be = 9 x 5 = 45
Step-by-step explanation:
Given that the Greatest Common Factor (GCF) of two whole numbers is 9.
Also the ratio is 6:5.
As we know that GCF is the greatest number that divides the two number.
So, if the ratio of two number is 6:5 then the greater number would be:
Greater number would be = 9 x 6 = 54
Smaller number would be = 9 x 5 = 45
Both the number have the ratio of 6:5 (54/45 = 6/5) and have a GCF of 9.
Keywords: Greatest Common Factor (GCF), ratio
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Answer:
A. 1/18
Step-by-step explanation: