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# Rational

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Determine and simplify the difference between 𝑥+2/ 4𝑥+8 and 3−𝑥/ x^2+2𝑥 . State any restrictions

Thank you!

Jun 7, 2021

#1
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$$\frac{x+2}{4x+8}-\frac{3-x}{x^2+2x}$$

$$\frac{(x+2)(x^2+2x)}{(4x+8)(x^2+2x)}-\frac{(3-x)(4x+8)}{(x^2+2x)(4x+8)}$$

$$\frac{x^3+4x^2+4x}{(4x+8)(x^2+2x)}-\frac{-4x^2+4x+24}{(x^2+2x)(4x+8)}$$

$$\frac{x^3+8x^2-24}{(x^2+2x)(4x+8)}$$

$$\frac{(x+2)(x^2+6x-12)}{x(x+2)(4x+8)}$$

$$\frac{x^2+6x-12}{4x^2+8x}$$

Restrictions: X cannot equal 0, -2, as these values would make the denominator 0.

Jun 7, 2021