Solve (x+4/3)(x+3/4)=x^2+25/12x+1

$$( x + \frac { 4 } { 3 } ) ( x + \frac { 3 } { 4 } ) = x ^ { 2 } + \frac { 25 } { 12 } x + 1$$

Solve for x (complex solution)

$$x\in \mathrm{C}$$

Solution Steps

Use the distributive property to multiply x+\frac{4}{3} by x+\frac{3}{4} and combine like terms.

$$x^{2}+\frac{25}{12}x+1=x^{2}+\frac{25}{12}x+1$$

Subtract x^{2} from both sides.

$$x^{2}+\frac{25}{12}x+1-x^{2}=\frac{25}{12}x+1$$

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

$$\frac{25}{12}x+1=\frac{25}{12}x+1$$

Subtract \frac{25}{12}x from both sides.

$$\frac{25}{12}x+1-\frac{25}{12}x=1$$

Combine \frac{25}{12}x and -\frac{25}{12}x to get 0.

$$1=1$$

Compare 1 and 1.

$$\text{true}$$

This is true for any x.

$$x\in \mathrm{C}$$

Solve for x

$$x\in \mathrm{R}$$

Solution Steps

Use the distributive property to multiply x+\frac{4}{3} by x+\frac{3}{4} and combine like terms.

$$x^{2}+\frac{25}{12}x+1=x^{2}+\frac{25}{12}x+1$$

Subtract x^{2} from both sides.

$$x^{2}+\frac{25}{12}x+1-x^{2}=\frac{25}{12}x+1$$

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

$$\frac{25}{12}x+1=\frac{25}{12}x+1$$

Subtract \frac{25}{12}x from both sides.

$$\frac{25}{12}x+1-\frac{25}{12}x=1$$

Combine \frac{25}{12}x and -\frac{25}{12}x to get 0.

$$1=1$$

Compare 1 and 1.

$$\text{true}$$

This is true for any x.

$$x\in \mathrm{R}$$