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megababe04
12.08.2020 •
Mathematics
pls help me need help asap
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Ответ:
The answer is
x² + 3x - 4Step-by-step explanation:
To solve the expression first factorize both the numerator and the denominator
For the numerator
9x² - ( x² - 4)²
Expand the terms in the bracket using the formula
( a - b)² = a² - 2ab + b²
(x² - 4) = x⁴ - 8x² + 16
So we have
9x² - (x⁴ - 8x² + 16)
9x² - x⁴ + 8x² - 16
- x⁴ + 17x² - 16
Factorize
that's
(x² - 16)(-x² + 1)
Using the formula
a² - b² = ( a + b)(a - b)
We have
(x² - 16)(-x² + 1) = (x + 4)(x - 4)( 1 - x)(1 + x)
For the denominator
- x² + 3x + 4
Write 3x as a difference
- x² + 4x - x + 4
Factorize
That's
- ( x - 4)(x + 1)
So we now have
Simplify
Reduce the expression by x + 1
That's
-( x + 4)( 1 - x)
Multiply the terms
We have the final answer as
x² + 3x - 4Hope this helps you
Ответ:
Step-by-step explanation:
Factor top and bottom.
The numerator is a difference of two squares, and the denominator is a quadratic.
=![\frac{ (3x+x^2-4)(3x-x^2+4) }{(1+x)(4-x)}](/tpl/images/0718/9355/0b6b5.png)
=![\frac{ (x-1)(x+4) (1+x)(4-x) }{(1+x)(4-x)}](/tpl/images/0718/9355/fc606.png)
If x does not equal -1 and does not equal 4, we can cancel the common factors in italics to give
=![{ (x-1)(x+4)}](/tpl/images/0718/9355/c967c.png)
=![{ x^2+3x-4}](/tpl/images/0718/9355/58dd7.png)
Ответ:
Step-by-step explanation: