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1)
![frac{5x^2}{x+5} - frac{6x^2-3x-30}{x+5} - frac{5-2x^2-7x}{x+5} = frac{5x^2-(6x^2-3x-30) - (5-2x^2-7x)}{x+5} = \ \
= frac{5x^2 -6x^2+3x+30 -5+2x^2+7x}{x+5} = frac{x^2+10x+25}{x+5} = \ \
=frac{x^2+2*x*5 +5^2}{x+5} = frac{(x+5)^2}{x+5} = frac{x+5}{1} = x+5](https://tex.z-dn.net/?f=+frac%7B5x%5E2%7D%7Bx%2B5%7D+-+frac%7B6x%5E2-3x-30%7D%7Bx%2B5%7D+-+frac%7B5-2x%5E2-7x%7D%7Bx%2B5%7D+%3D++frac%7B5x%5E2-%286x%5E2-3x-30%29+-+%285-2x%5E2-7x%29%7D%7Bx%2B5%7D+%3D+%5C++%5C+%0A%3D+frac%7B5x%5E2+-6x%5E2%2B3x%2B30+-5%2B2x%5E2%2B7x%7D%7Bx%2B5%7D+%3D++frac%7Bx%5E2%2B10x%2B25%7D%7Bx%2B5%7D+%3D++%5C++%5C+%0A%3Dfrac%7Bx%5E2%2B2%2Ax%2A5+%2B5%5E2%7D%7Bx%2B5%7D+%3D++frac%7B%28x%2B5%29%5E2%7D%7Bx%2B5%7D+%3D++frac%7Bx%2B5%7D%7B1%7D+%3D+x%2B5 "frac{5x^2}{x+5} - frac{6x^2-3x-30}{x+5} - frac{5-2x^2-7x}{x+5} = frac{5x^2-(6x^2-3x-30) - (5-2x^2-7x)}{x+5} = \ \
= frac{5x^2 -6x^2+3x+30 -5+2x^2+7x}{x+5} = frac{x^2+10x+25}{x+5} = \ \
=frac{x^2+2*x*5 +5^2}{x+5} = frac{(x+5)^2}{x+5} = frac{x+5}{1} = x+5")
2)
![frac{a^2}{a-2} - frac{a^2}{a+2} - frac{16}{a^2-4} = frac{a^2(a+2)-a^2(a-2)-16}{a^2-2^2} = \ \
=frac{a^3+2a^2 - a^3+2a^2 - 16}{(a-2)(a+2)} = frac{4a^2-16}{a^2-2^2} = frac{4(a^2-4)}{a^2-4} =4](https://tex.z-dn.net/?f=+frac%7Ba%5E2%7D%7Ba-2%7D+-+frac%7Ba%5E2%7D%7Ba%2B2%7D+-+frac%7B16%7D%7Ba%5E2-4%7D+%3D+frac%7Ba%5E2%28a%2B2%29-a%5E2%28a-2%29-16%7D%7Ba%5E2-2%5E2%7D+%3D+++%5C++%5C+%0A%3Dfrac%7Ba%5E3%2B2a%5E2+-+a%5E3%2B2a%5E2+-+16%7D%7B%28a-2%29%28a%2B2%29%7D+%3D++frac%7B4a%5E2-16%7D%7Ba%5E2-2%5E2%7D+%3D++frac%7B4%28a%5E2-4%29%7D%7Ba%5E2-4%7D+%3D4 "frac{a^2}{a-2} - frac{a^2}{a+2} - frac{16}{a^2-4} = frac{a^2(a+2)-a^2(a-2)-16}{a^2-2^2} = \ \
=frac{a^3+2a^2 - a^3+2a^2 - 16}{(a-2)(a+2)} = frac{4a^2-16}{a^2-2^2} = frac{4(a^2-4)}{a^2-4} =4")
3)
![frac{x}{x+3} + frac{3x}{x+3} + frac{12x+36}{x^2+6x+9} = frac{x+3x}{x+3} + frac{12(x+3)}{x^2+2*x*3+3^2} = \ \
= frac{4x}{x+3} + frac{12(x+3)}{(x+3)^2} = frac{4x}{x+3} + frac{12}{x+3}= \ \
= frac{4x+12}{x+3} = frac{4(x+3)}{x+3} = 4](https://tex.z-dn.net/?f=+frac%7Bx%7D%7Bx%2B3%7D+%2B+frac%7B3x%7D%7Bx%2B3%7D+%2B+frac%7B12x%2B36%7D%7Bx%5E2%2B6x%2B9%7D+%3D++frac%7Bx%2B3x%7D%7Bx%2B3%7D+%2B+frac%7B12%28x%2B3%29%7D%7Bx%5E2%2B2%2Ax%2A3%2B3%5E2%7D+%3D++%5C++%5C+%0A%3D++frac%7B4x%7D%7Bx%2B3%7D+%2B++frac%7B12%28x%2B3%29%7D%7B%28x%2B3%29%5E2%7D+%3D++frac%7B4x%7D%7Bx%2B3%7D+%2B++frac%7B12%7D%7Bx%2B3%7D%3D+%5C++%5C+%0A%3D+frac%7B4x%2B12%7D%7Bx%2B3%7D+%3D+frac%7B4%28x%2B3%29%7D%7Bx%2B3%7D+%3D+4 "frac{x}{x+3} + frac{3x}{x+3} + frac{12x+36}{x^2+6x+9} = frac{x+3x}{x+3} + frac{12(x+3)}{x^2+2*x*3+3^2} = \ \
= frac{4x}{x+3} + frac{12(x+3)}{(x+3)^2} = frac{4x}{x+3} + frac{12}{x+3}= \ \
= frac{4x+12}{x+3} = frac{4(x+3)}{x+3} = 4")
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