Solving the Equation: (x+1)(4x3)4x^2+5/4x+1=2
This article will guide you through the steps of solving the given equation: (x+1)(4x3)4x^2+5/4x+1=2.
Simplifying the Equation

Expand the product: Start by expanding the product (x+1)(4x3) using the distributive property (or FOIL method): (x+1)(4x3) = 4x²  3x + 4x  3 = 4x² + x  3

Rewrite the equation: Now, substitute this expansion back into the original equation: 4x² + x  3  4x² + 5/4x + 1 = 2

Combine like terms: Notice that the terms 4x² and 4x² cancel each other out. Combine the remaining terms: x + 5/4x  2 = 2

Simplify the fraction: To combine the 'x' terms, we need a common denominator. Multiply the first 'x' term by 4/4: (4/4)x + 5/4x  2 = 2 9/4x  2 = 2
Solving for 'x'

Isolate the 'x' term: Add 2 to both sides of the equation: 9/4x = 4

Multiply both sides by the reciprocal: Multiply both sides by 4/9, the reciprocal of 9/4, to isolate 'x': (4/9) * (9/4)x = 4 * (4/9) x = 16/9
Solution
Therefore, the solution to the equation (x+1)(4x3)4x^2+5/4x+1=2 is x = 16/9.