What is the simplest common denominator of fractions x 2 - x 1, x 2 - 2 x + 1, and X + x 2 1-x?

What is the simplest common denominator of fractions x 2 - x 1, x 2 - 2 x + 1, and X + x 2 1-x?

Because the three denominators x? - x = x (x-1), x? - 2x + 1 = (x-1) ^ 2, x + X? = x (1 + x), the simplest common denominator is
x(x-1)^2(x+1).

Fraction 3 2(x+1)，2x 5(1−x)，1−2x The simplest common denominator of x2 − 1 is______ .

The least common multiple of 2, 5, 1 is 10, and the common factor of three fractions is (x + 1) (x-1). Therefore, the simplest common denominator is 10 (x + 1) (x-1)

What is the simplest common denominator of fractions 2 / 1-x? 2, 1 / x? - 2x + 1, 3 / x? 2 + X-2?

1-x²=(1+x)(1-x)
x²-2x+1=(1-x)(1-x)
x²+x-2=(x-1)(x+2)
simplest common denominator
(x-1)²(x+2)(x+1)

What is the simplest common denominator of the fraction 2-x / x? - x, X-2 / x? + X, X-2 / (x-1) 3? Explain the reason!

x²-x=x(x-1)
x²+x=x(x+1)
(x-1)³
Therefore, the simplest common denominator is: X (x + 1) (x-1) 3

Given that x2-3x + 1 = 0, find x2 X4 + 3x2 + 1

x2-3x+1=0，
Divide both sides by X at the same time to get x-3 + 1
x=0，
X+1
x=3，
Two sides squared, X2 + 2 + 1
x2=9，
That is, X2 + 1
x2=7，
Original formula = 1
x2+3+1
x2=1
7+3=1
10．

What conditions must x satisfy in order to make the radical 2x-5-radical 3-x meaningful?

Greater than or equal to 0 under root sign
2x-5≥0
x≥5/2
3-x≥0
x≤3
5/2≤x≤3

What makes the root sign 2x + 5 meaningful is that

The denominator is not 0  X-2 ≠ 0  x ≠ 2
Even power root, the opened mode is non negative  2x + 5 ≥ 0  x ≥ - 5 / 2
ν x ≥ - 5 / 2 and X ≠ 2

Make the root sign 2x + 3 and the root sign 4-x of X have significance. The value range of X Another problem is that the solution of the equation AX + 12 = 0 of X is x = 3. Please make sure that the solution set of (a + 2) x ＞ - 8 is urgent

(1) ∵ the root sign 2x + 3 and the root sign 4-x of X are meaningful
/ / 2x + 3 ≥ 0 (the number of square root cannot be negative) (1)
X ≠ 0 (denominator is not 0) II.
4-x ≥ 0 (same as ①)
ν - 3 / 2 ≤ x ≤ 4 and X ≠ 0
(2) ∵ the solution of AX + 12 = 0 is x = 3
∴3a+12=0
a=-4
∴（a+2）X＞-8
It can be converted into: (- 4 + 2) x ＞ - 8
-2X＞-8
X＜4

If the formula (radical 2x-1) - (radical 1-2x + 1) is meaningful, then the value range of X is

∵ meaningful
/ / 2x-1 > = 0 and 1-2x > = 0
∴x=1/2

Find the value of quadratic radical: root sign (1 + 2x + x 2), where x = - radical 2

Where x = - radical 2
The root sign (1 + 2x + x 2) = √ (x + 1) 2 = √ (1 - √ 2) 2 = √ 2-1;
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