Solve k-2/k+3=k-3/k+7

$$\frac { k - 2 } { k + 3 } = \frac { k - 3 } { k + 7 }$$

Solve for k

$$k=1$$

Steps for Solving Linear Equation

Variable k cannot be equal to any of the values -7,-3 since division by zero is not defined. Multiply both sides of the equation by \left(k+3\right)\left(k+7\right), the least common multiple of k+3,k+7.

$$\left(k+7\right)\left(k-2\right)=\left(k+3\right)\left(k-3\right)$$

Use the distributive property to multiply k+7 by k-2 and combine like terms.

$$k^{2}+5k-14=\left(k+3\right)\left(k-3\right)$$

Consider \left(k+3\right)\left(k-3\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Square 3.

$$k^{2}+5k-14=k^{2}-9$$

Subtract k^{2} from both sides.

$$k^{2}+5k-14-k^{2}=-9$$

Combine k^{2} and -k^{2} to get 0.

$$5k-14=-9$$

Add 14 to both sides.

$$5k=-9+14$$

Add -9 and 14 to get 5.

$$5k=5$$

Divide both sides by 5.

$$k=\frac{5}{5}$$

Divide 5 by 5 to get 1.

$$k=1$$