Algebra Examples

$X^{2} - 4 N X + 4 M > 0$

Step 1

Move all terms not containing $N$ to the right side of the inequality.

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Step 1.1

Subtract $X^{2}$ from both sides of the inequality.

$- 4 N X + 4 M > - X^{2}$

Step 1.2

Subtract $4 M$ from both sides of the inequality.

$- 4 N X > - X^{2} - 4 M$

Step 2

Divide each term in $- 4 N X > - X^{2} - 4 M$ by $- 4 X$ and simplify.

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Step 2.1

Divide each term in $- 4 N X > - X^{2} - 4 M$ by $- 4 X$ .

$\frac{- 4 N X}{- 4 X} > \frac{- X^{2}}{- 4 X} + \frac{- 4 M}{- 4 X}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $- 4$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{- 4 N X}{- 4 X} > \frac{- X^{2}}{- 4 X} + \frac{- 4 M}{- 4 X}$

Step 2.2.1.2

Rewrite the expression.

$\frac{N X}{X} > \frac{- X^{2}}{- 4 X} + \frac{- 4 M}{- 4 X}$

Step 2.2.2

Cancel the common factor of $X$ .

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Step 2.2.2.1

Cancel the common factor.

$\frac{N X}{X} > \frac{- X^{2}}{- 4 X} + \frac{- 4 M}{- 4 X}$

Step 2.2.2.2

Divide $N$ by $1$ .

$N > \frac{- X^{2}}{- 4 X} + \frac{- 4 M}{- 4 X}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Simplify each term.

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Step 2.3.1.1

Cancel the common factor of $X^{2}$ and $X$ .

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Step 2.3.1.1.1

Factor $X$ out of $- X^{2}$ .

$N > \frac{X (- X)}{- 4 X} + \frac{- 4 M}{- 4 X}$

Step 2.3.1.1.2

Cancel the common factors.

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Step 2.3.1.1.2.1

Factor $X$ out of $- 4 X$ .

$N > \frac{X (- X)}{X \cdot - 4} + \frac{- 4 M}{- 4 X}$

Step 2.3.1.1.2.2

Cancel the common factor.

$N > \frac{X (- X)}{X \cdot - 4} + \frac{- 4 M}{- 4 X}$

Step 2.3.1.1.2.3

Rewrite the expression.

$N > \frac{- X}{- 4} + \frac{- 4 M}{- 4 X}$

Step 2.3.1.2

Dividing two negative values results in a positive value.

$N > \frac{X}{4} + \frac{- 4 M}{- 4 X}$

Step 2.3.1.3

Cancel the common factor of $- 4$ .

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Step 2.3.1.3.1

Cancel the common factor.

$N > \frac{X}{4} + \frac{- 4 M}{- 4 X}$

Step 2.3.1.3.2

Rewrite the expression.

$N > \frac{X}{4} + \frac{M}{X}$