Simplify ((2c-2d)^2)/((3c-3d)^2)

$\frac{{(2 c - 2 d)}^{2}}{{(3 c - 3 d)}^{2}}$

Step 1

Simplify the numerator.

Factor $2$ out of $2 c - 2 d$ .

Factor $2$ out of $2 c$ .

$\frac{{(2 (c) - 2 d)}^{2}}{{(3 c - 3 d)}^{2}}$

Factor $2$ out of $- 2 d$ .

$\frac{{(2 (c) + 2 (- d))}^{2}}{{(3 c - 3 d)}^{2}}$

Factor $2$ out of $2 (c) + 2 (- d)$ .

$\frac{{(2 (c - d))}^{2}}{{(3 c - 3 d)}^{2}}$

$\frac{{(2 (c - d))}^{2}}{{(3 c - 3 d)}^{2}}$

Apply the product rule to $2 (c - d)$ .

$\frac{2^{2} {(c - d)}^{2}}{{(3 c - 3 d)}^{2}}$

Raise $2$ to the power of $2$ .

$\frac{4 {(c - d)}^{2}}{{(3 c - 3 d)}^{2}}$

$\frac{4 {(c - d)}^{2}}{{(3 c - 3 d)}^{2}}$

Step 2

Simplify the denominator.

Factor $3$ out of $3 c - 3 d$ .

Factor $3$ out of $3 c$ .

$\frac{4 {(c - d)}^{2}}{{(3 (c) - 3 d)}^{2}}$

Factor $3$ out of $- 3 d$ .

$\frac{4 {(c - d)}^{2}}{{(3 (c) + 3 (- d))}^{2}}$

Factor $3$ out of $3 (c) + 3 (- d)$ .

$\frac{4 {(c - d)}^{2}}{{(3 (c - d))}^{2}}$

$\frac{4 {(c - d)}^{2}}{{(3 (c - d))}^{2}}$

Apply the product rule to $3 (c - d)$ .

$\frac{4 {(c - d)}^{2}}{3^{2} {(c - d)}^{2}}$

Raise $3$ to the power of $2$ .

$\frac{4 {(c - d)}^{2}}{9 {(c - d)}^{2}}$

$\frac{4 {(c - d)}^{2}}{9 {(c - d)}^{2}}$

Step 3

Cancel the common factor of ${(c - d)}^{2}$ .

Cancel the common factor.

$\frac{4 {(c - d)}^{2}}{9 {(c - d)}^{2}}$

Rewrite the expression.

$\frac{4}{9}$

$\frac{4}{9}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{4}{9}$

Decimal Form:

$0.\overline{4}$

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