Find Where Undefined/Discontinuous (m^2-2m+1)/(2m^2+m-3)

$\frac{m^{2} - 2 m + 1}{2 m^{2} + m - 3}$

Step 1

Set the denominator in $\frac{m^{2} - 2 m + 1}{2 m^{2} + m - 3}$ equal to $0$ to find where the expression is undefined.

$2 m^{2} + m - 3 = 0$

Step 2

Solve for $m$ .

Factor by grouping.

For a polynomial of the form $a x^{2} + b x + c$ , rewrite the middle term as a sum of two terms whose product is $a \cdot c = 2 \cdot - 3 = - 6$ and whose sum is $b = 1$ .

Multiply by $1$ .

$2 m^{2} + 1 m - 3 = 0$

Rewrite $1$ as $- 2$ plus $3$

$2 m^{2} + (- 2 + 3) m - 3 = 0$

Apply the distributive property.

$2 m^{2} - 2 m + 3 m - 3 = 0$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(2 m^{2} - 2 m) + 3 m - 3 = 0$

Factor out the greatest common factor (GCF) from each group.

$2 m (m - 1) + 3 (m - 1) = 0$

Factor the polynomial by factoring out the greatest common factor, $m - 1$ .

$(m - 1) (2 m + 3) = 0$

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$m - 1 = 0$

$2 m + 3 = 0$

Set $m - 1$ equal to $0$ and solve for $m$ .

Set $m - 1$ equal to $0$ .

$m - 1 = 0$

Add $1$ to both sides of the equation.

$m = 1$

Set $2 m + 3$ equal to $0$ and solve for $m$ .

Set $2 m + 3$ equal to $0$ .

$2 m + 3 = 0$

Solve $2 m + 3 = 0$ for $m$ .

Subtract $3$ from both sides of the equation.

$2 m = - 3$

Divide each term in $2 m = - 3$ by $2$ and simplify.

Divide each term in $2 m = - 3$ by $2$ .

$\frac{2 m}{2} = \frac{- 3}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 m}{2} = \frac{- 3}{2}$

Divide $m$ by $1$ .

$m = \frac{- 3}{2}$

Simplify the right side.

Move the negative in front of the fraction.

$m = - \frac{3}{2}$

The final solution is all the values that make $(m - 1) (2 m + 3) = 0$ true.

$m = 1, - \frac{3}{2}$

Step 3

The equation is undefined where the denominator equals $0$ , the argument of a square root is less than $0$ , or the argument of a logarithm is less than or equal to $0$ .

$m = - \frac{3}{2}, m = 1$

Step 4

Find Where Undefined/Discontinuous (m^2-2m+1)/(2m^2+m-3)

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