Respuesta :
Answer:
(2x + 8)/(x² + 2x - 8)
Step-by-step explanation:
When fractions have a common denominator, we can add or subtract the numerators. (Since the 2 fractions share the same denominator, we will ignore it for now...)
Subtracting the two numerators give us...
x² - x + 3 - (x² - 3x - 5)
x² - x + 3 - x² - (-3x) - (-5)
x² - x + 3 - x² + 3x + 5
2x + 8
So the final answer is (2x + 8)/(x² + 2x - 8)
After subtracting the given two expressions, we get [tex]\frac{2x+8 }{x^{2}+2x - 8 }[/tex]
How to subtract the given two expressions ?
The two expressions given are [tex]\frac{x^{2}-x+3}{x^{2}+2x - 8 }[/tex] and [tex]\frac{x^{2}-3x-5}{x^{2}+2x - 8 }[/tex]
For subtracting these two equations, we find the L.C.M(Least Common Factor) and then multiply the numerator to suitable value and then perform the subtraction.
As we can see the common L.C.M in both the terms is [tex]x^{2} + 2x - 8[/tex]
Now performing the subtraction,
= [tex]\frac{x^{2}-x+3}{x^{2}+2x - 8 }[/tex] - [tex]\frac{x^{2}-3x-5}{x^{2}+2x - 8 }[/tex]
= [tex]\frac{(x^{2} - x^{2}) + (3x - x) + (5 + 3)}{x^{2}+2x - 8 }[/tex]
= [tex]\frac{2x+8 }{x^{2}+2x - 8 }[/tex]
Therefore we get the subtracted expression as [tex]\frac{2x+8 }{x^{2}+2x - 8 }[/tex].
To learn more about subtraction of expression, refer -
https://brainly.com/question/1918916
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