\frac{x^{2}+3x-28}{x^{2}+4x+4}+\frac{x^{2}-5x-14}{x^{2}-49}

glasskerfu

glasskerfu

Answered question

2021-09-20

x2+3x28x2+4x+4+x25x14x249

Answer & Explanation

Cristiano Sears

Cristiano Sears

Skilled2021-09-21Added 96 answers

Find the factors of each quadratic,
(x+7)(x4)(x+2)(x+2)+(x7)(x+2)(x7)(x+7)
By canceling common term from numerator and denominator,
(x+7)(x4)(x+2)(x+2)+(x+2)(x+7)
Step 2
The addition of fractions is possible only when they have the same denominators.
Here least common denominator is (x+2)(x+2)(x+7).
Make the denominator of each fraction to be (x+2)(x+2)(x+7).
(x+7)(x4)(x+7)(x+2)(x+2)(x+7)+(x+2)(x+2)(x+2)(x+7)(x+2)(x+2)
Now the denominators are the same, add numerators and keep denominators as it is.
(x+7)(x4)(x+7)+(x+2)(x+2)(x+2)(x+2)(x+2)(x+7)
Distribute the numerator,
x3+10x27x196+x3+6x2+12x+8(x+2)(x+2)(x+7)
Combine like terms,
2x3+16x2+5x188(x+2)(x+2)(x+7)
It can be written as,
2x3+16x2+5x188(x+2)2(x+7)
The sum of the fractions
x2+3x28x2+4x+4+x25x14x249=2x3+16x2+5x188(x+2)2

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