4 3 2
2x+7/2x+21x+35x-37x+46
Don't forget the workout & the explanation please!👍
What is the numerator and what is the denominator?
If something is squared write
x^2
cubed write x^3
(2x^4 + 7) maybe ????
If you mean
(2x+7)/(2x^4+21x^3+35x^2-37x+46) then that is approximately
(2x+7)/((x+7.966203)(x+3.527066)(2x^2-1.98654x+1.63717))
Now you can just use partial fractions on that mess.
To simplify the expression (2x+7)/(2x+21) + (35x-37)/(x+46), we need to find a common denominator and combine the fractions.
Step 1: Factor the denominators as much as possible.
The first denominator, 2x+21, can be factored as 1 * (2x + 21).
The second denominator, x+46, cannot be factored further.
Step 2: Determine the least common multiple (LCM) of the denominators.
Since 2x+21 and x+46 don't share any common factors (aside from 1), the LCM is simply the product of the two denominators: (2x+21)(x+46).
Step 3: Rewrite the fractions with the common denominator.
To do this, we need to multiply the numerator and denominator of each fraction by the appropriate factors to obtain the common denominator.
For the first fraction, we multiply the numerator and denominator by (x+46):
[(2x+7)(x+46)] / [(2x+21)(x+46)]
For the second fraction, we multiply the numerator and denominator by 1:
[(35x-37)(1)] / [(x+46)(1)]
Step 4: Combine the fractions.
Now that we have the same denominator for both fractions, we can add the numerators together while keeping the denominator unchanged:
[(2x+7)(x+46) + (35x-37)] / [(2x+21)(x+46)]
Step 5: Simplify further if possible.
Expand the numerator by distributing:
(2x^2 + 69x + 322 + 35x - 37) / [(2x+21)(x+46)]
Combine like terms in the numerator:
(2x^2 + 104x + 285) / [(2x+21)(x+46)]
Step 6: Check if the expression can be simplified further.
At this point, we cannot simplify the expression any further since there are no common factors in the numerator and denominator. Thus, the final simplified expression is:
(2x^2 + 104x + 285) / [(2x+21)(x+46)]
That's the step-by-step explanation of how to simplify the given expression.