Simplify the complex fraction
((3x-7)/x^2)/(x^2/2)+(2/x)
Is this answer right?
(6x-14-2x^3)/(x^4)
How did you get that minus ?
I had (6x - 14 + 2x^3)/x^4
You make little mistake.
[ ( 3 x - 7 ) / x² ] / ( x² / 2 ) + 2 / x =
2 • ( 3 x - 7 ) / ( x² • x² ) + 2 / x=
( 6 x - 14 ) / x⁴ + 2 / x =
( 6 x - 14 ) / x⁴ + 2 • x³ / x⁴=
( 2 x³ + 6 x - 14 ) / x⁴ =
2 ( x³ + 3 x - 7 ) / x⁴
"I'm confused" you make mistake, not mathhelper.
Bosnian is correct, he simply factored out the 2 for a better answer
To simplify the given complex fraction, we need to follow these steps:
Step 1: Find the LCD (Least Common Denominator) of all the fractions involved.
The denominators in the given expression are x^2, 2, and x. To find the LCD, we need to factorize x^2 and look for the highest power of each factor. In this case, the highest power of x is 2 and the highest power of 2 is 1. So, the LCD is x^2 * 2, which is equal to 2x^2.
Step 2: Express each fraction with the LCD as the denominator.
For the fraction (3x-7)/x^2, we multiply both the numerator and the denominator by 2x^2 to get:
((3x-7)(2x^2))/(x^2 * 2x^2)
Simplifying the numerator gives us: (6x^3 - 14x^2)
For the fraction x^2/2, we also multiply both the numerator and the denominator by x^2 to get: (x^4)/(2x^2)
And for the fraction 2/x, we multiply both the numerator and the denominator by 2x^2 to get: (4x^2)/(2x^2)
Step 3: Combine the fractions.
Now, we can rewrite the complex fraction:
((3x-7)(2x^2))/(x^2 * 2x^2) + (x^4)/(2x^2) + (4x^2)/(2x^2)
Simplifying further:
(6x^3 - 14x^2)/(2x^4) + (x^4)/(2x^2) + (4x^2-14x^2)/(2x^2)
Combine the like terms in each fraction:
(6x^3 - 14x^2)/(2x^4) + (x^4)/(2x^2) + (-10x^2)/(2x^2)
Simplifying the expressions in the numerators and the denominators:
(6x^3 - 14x^2)/(2x^4) + (x^4)/(2x^2) - (10x^2)/(2x^2)
Combining the numerators:
(6x^3 - 14x^2 + x^4 - 10x^2)/(2x^4)
Rearranging the terms in descending order of powers of x:
(x^4 + 6x^3 - 24x^2)/(2x^4)
So, the simplified form of the given complex fraction is:
(x^4 + 6x^3 - 24x^2)/(2x^4)
Therefore, the answer you provided, (6x-14-2x^3)/(x^4), is not correct.