7. Simplify, State any restrictions on the variables. (3)/(x+1)+(1)/(x^2)-3x-4 b) (2t)/(t-4)-(5t)/(t^2)-16 c) (3)/(t^2)+t-6+(5)/((t+3)^2) d) (4x)/(x^2)+6x+8-(3x)/(x^2)-3x-10 c) (x-1)/(x^2)-9+(x+7)/(x^2)-5x+6 (2t+1)/(2t^2)-14t+24+(5t)/(4t^2)-8t-12

## Step 1: Factor the denominators### Factor each denominator to find the least common denominator (LCD). For example, and . Similarly, , , , , , , and .## Step 2: Find the least common denominator (LCD)### Identify the LCD by considering all unique factors in the denominators. For a), the LCD is . For b), the LCD is . For c), the LCD is . For d), the LCD is . For e), the LCD is . For f), the LCD is .## Step 3: Rewrite each fraction with the LCD### Multiply each fraction by a form of 1 so that each fraction has the LCD. For example, in a), multiply by .## Step 4: Combine the numerators### Add or subtract the numerators over the common denominator. Simplify the resulting numerator by combining like terms.## Step 5: Simplify the resulting fraction### Factor the numerator if possible and cancel any common factors between the numerator and denominator.## Step 6: State any restrictions### Identify any values of the variable that would make the denominator zero in the original expression or any intermediate step. These values are the restrictions on the variable.