Algebra Examples

$2 (x + 1) {(x - 1)}^{- 1} - {(x + 1)}^{2} {(x - 1)}^{- 2} + 3 (x + 1) {(x - 1)}^{- 2}$

Step 1

Factor $(x + 1) {(x - 1)}^{- 2}$ out of $2 (x + 1) {(x - 1)}^{- 1} - {(x + 1)}^{2} {(x - 1)}^{- 2} + 3 (x + 1) {(x - 1)}^{- 2}$ .

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Step 1.1

Factor $(x + 1) {(x - 1)}^{- 2}$ out of $2 (x + 1) {(x - 1)}^{- 1}$ .

$(x + 1) {(x - 1)}^{- 2} (2 (x - 1)) - {(x + 1)}^{2} {(x - 1)}^{- 2} + 3 (x + 1) {(x - 1)}^{- 2}$

Step 1.2

Factor $(x + 1) {(x - 1)}^{- 2}$ out of $- {(x + 1)}^{2} {(x - 1)}^{- 2}$ .

$(x + 1) {(x - 1)}^{- 2} (2 (x - 1)) + (x + 1) {(x - 1)}^{- 2} (- (x + 1)) + 3 (x + 1) {(x - 1)}^{- 2}$

Step 1.3

Factor $(x + 1) {(x - 1)}^{- 2}$ out of $3 (x + 1) {(x - 1)}^{- 2}$ .

$(x + 1) {(x - 1)}^{- 2} (2 (x - 1)) + (x + 1) {(x - 1)}^{- 2} (- (x + 1)) + (x + 1) {(x - 1)}^{- 2} (3)$

Step 1.4

Factor $(x + 1) {(x - 1)}^{- 2}$ out of $(x + 1) {(x - 1)}^{- 2} (2 (x - 1)) + (x + 1) {(x - 1)}^{- 2} (- (x + 1))$ .

$(x + 1) {(x - 1)}^{- 2} (2 (x - 1) - (x + 1)) + (x + 1) {(x - 1)}^{- 2} (3)$

Step 1.5

Factor $(x + 1) {(x - 1)}^{- 2}$ out of $(x + 1) {(x - 1)}^{- 2} (2 (x - 1) - (x + 1)) + (x + 1) {(x - 1)}^{- 2} (3)$ .

$(x + 1) {(x - 1)}^{- 2} (2 (x - 1) - (x + 1) + 3)$

Step 2

Apply the distributive property.

$(x + 1) {(x - 1)}^{- 2} (2 x + 2 \cdot - 1 - (x + 1) + 3)$

Step 3

Multiply $2$ by $- 1$ .

$(x + 1) {(x - 1)}^{- 2} (2 x - 2 - (x + 1) + 3)$

Step 4

Apply the distributive property.

$(x + 1) {(x - 1)}^{- 2} (2 x - 2 - x - 1 \cdot 1 + 3)$

Step 5

Multiply $- 1$ by $1$ .

$(x + 1) {(x - 1)}^{- 2} (2 x - 2 - x - 1 + 3)$

Step 6

Subtract $x$ from $2 x$ .

$(x + 1) {(x - 1)}^{- 2} (x - 2 - 1 + 3)$

Step 7

Subtract $1$ from $- 2$ .

$(x + 1) {(x - 1)}^{- 2} (x - 3 + 3)$

Step 8

Add $- 3$ and $3$ .

$(x + 1) {(x - 1)}^{- 2} (x + 0)$

Step 9

Add $x$ and $0$ .

$(x + 1) {(x - 1)}^{- 2} x$