3 years ago

When you apply addition, add both side of the equation. Which property of equality is it

Mathematics

1 answer:

Nikolay [14]3 years ago

8 0

I think addition property of equality

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F(x+1)+f(x+2)=2x+3; f(x)=?

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Answer:

$F=\frac{-xf+f+2x}{x+1};\quad \:x\ne \:-1$

Step-by-step explanation:

$1. \mathrm{Subtract\:}f\left(x+2\right)\mathrm{\:from\:both\:sides}\\
F\left(x+1\right)+f\left(x+2\right)-f\left(x+2\right)=2x+3f-f\left(x+2\right)

$

$2. \mathrm{Simplify}\\
F\left(x+1\right)=-xf+f+2x\\
$

$3. \mathrm{Divide\:both\:sides\:by\:}x+1;\quad \:x\ne \:-1\\
\frac{F\left(x+1\right)}{x+1}=-\frac{xf}{x+1}+\frac{f}{x+1}+\frac{2x}{x+1};\quad \:x\ne \:-1$

$4. \mathrm{Simplify}\\
F=\frac{-xf+f+2x}{x+1};\quad \:x\ne \:-1$

Final Answer: $F=\frac{-xf+f+2x}{x+1};\quad \:x\ne \:-1$

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