Question

Wykonaj działania:
a)x/x-4 : x²-16
b) x+1/x-1 : x²+x/3x-3
c)4/x+2 + 3/x-1
d)1/x²+ 2x+1 - 3x/x+1

Answer 1

{a}/{b} ---> ułamek a przez b
x^3 ----> x do potęgi 3

a)
{x}/{x-4} : {x²-16} = {x}/{x-4} * {1}/{x²-16} = {x}/{(x-4)(x²-16)} =
= {x}/{x^3 - 4x² - 16x + 64}
b)
{x+1}/{x-1} : {x²+x}/{3x-3} = {x+1}/{x-1} * {3x-3}/{x²+x} =
= {x+1}/{x-1} * {3(x-1)}/{x(x+1)} = {3}/{x}
c)
{4}/{x+2} + {3}/{x-1} = {4(x-1)+3(x+2)}/{(x+2)(x-1)} =
= {4x-4+3x+6}/{(x+2)(x-1)} = {7x+2}/{(x+2)(x-1)}
d)
{1}/{x²}+ 2x+1 - {3x}/{x+1} = {1(x+1)+(2x+1)x²(x+1)-3x(x²)}/{x²(x+1)} =
= {x+1+(2x^3 +x²)(x+1)-3x^3}/{x²(x+1)} =
{x+1+2x^4 +3x^3 +x²-3x^3}/{x²(x+1)} = {2x^4 +x² +x+1}/{x²(x+1)}

Answer 2

A)
x/x-4 : x²-16
x/x-4 : (x-4)(x+4) // Skracamy (x-4)
x/(x +4)

b)
x+1/x-1 : x²+x/3x-3
x+1/x-1 : x(x+1)/3(x-1)
x+1/x-1 * 3(x-1)/x(x+1)
1 * 3/x
3/x

c)
4/x+2 + 3/x-1
4/x+2 *1 + 3/x-1 *1
4 (x-1)/ (x+2)(x-1) + 3(x+2)/(x+2)(x-1)
4x-4/(x²+x-2) +3x+6/(x²+x-2)
4x-4+3x+6/(x²+x-2)
7x +2/(x²+x-2)

d)
1/x²+ 2x+1 - 3x/x+1
(x+1)/(x³+x²) + (2x+1)(x³+x²)/(x³+x²)-3x *x²/(x³+x²)
(x+1)/x³+x² + 2x⁴+2x³+x³+x²/x³+x² - 3x³/x³+x²
x+1/x³+x² +2x⁴+3x³+x²/x³+x² - 3x³/x³+x²
x+1 +2x⁴+3x³ +x² -3x³/x³+x²
2x⁴+x² +x +2/(x³+x²)