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Solving Rational Functions Zoom in for a closer look Please help I've been stuck for awhile ​

Solving Rational Functions Zoom In For A Closer Look Please Help Ive Been Stuck For Awhile class=

Sagot :

Answer:

x = 4

Step-by-step explanation:

Given

[tex]\frac{3}{x+4}[/tex] - [tex]\frac{1}{x+3}[/tex] = [tex]\frac{x+9}{x^2+7x+12}[/tex] ← factor the quadratic

[tex]\frac{3}{x+4}[/tex] - [tex]\frac{1}{x+3}[/tex] = [tex]\frac{x+9}{(x+3)(x+4)}[/tex]

Multiply through by (x + 3)(x + 4) to clear the fractions

3(x+3) - (x + 4) = x + 9 ← distribute and simplify left side

3x + 9 - x - 4 = x + 9

2x + 5 = x + 9 ( subtract x from both sides )

x + 5 = 9 ( subtract 5 from both sides )

x = 4

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