Question 3 Solve the equation (x)/(x-1)+(2)/(5)=(3)/(2)

Find Common Denominator: To solve the equation (x)/(x-1) + (2)/(5) = (3)/(2), we need to find a common denominator for the fractions on the left side of the equation. The common denominator for (x-1) and 5 is 5(x-1).Eliminate Fractions: Multiply each term by the common denominator 5(x-1) to eliminate the fractions: 5(x-1) * (x)/(x-1) + 5(x-1) * (2)/(5) = 5(x-1) * (3)/(2).Simplify Terms: Simplify each term: 5x + 2(x-1) = (3/2) * 5(x-1).Combine Like Terms: Distribute the 2 and the (3/2) * 5 across the respective parentheses: 5x + 2x - 2 = (15/2)(x-1).Distribute Right Side: Combine like terms on the left side of the equation: 7x - 2 = (15/2)(x-1).Clear Fractions: Distribute the (15/2) on the right side of the equation: 7x - 2 = (15/2)x - (15/2).Simplify Equation: Multiply every term by 2 to clear the fraction on the right side of the equation: 2(7x) - 2(2) = 2((15/2)x) - 2((15/2)).Isolate Variable: Simplify the equation: 14x - 4 = 15x - 15.Solve for x: Subtract 14x from both sides to get the x terms on one side: -4 = x - 15.Add 15 to both sides to solve for x: x = 11.

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Question 3
Solve the equation
(x)/(x-1)+(2)/(5)=(3)/(2)

Question $3$ $\newline$ Solve the equation $\frac{x}{x-1}+\frac{2}{5}=\frac{3}{2}$

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Algebra 2

Sum of finite series starts from 1

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Solve the equation

\frac{x}{x-1}+\frac{2}{5}=\frac{3}{2}

Find Common Denominator: To solve the equation $(x)/(x-1) + (2)/(5) = (3)/(2)$ , we need to find a common denominator for the fractions on the left side of the equation. The common denominator for $(x-1)$ and $5$ is $5(x-1)$ .
Eliminate Fractions: Multiply each term by the common denominator $5(x-1)$ to eliminate the fractions: $\newline$ $5(x-1) \times \frac{x}{(x-1)} + 5(x-1) \times \frac{2}{5} = 5(x-1) \times \frac{3}{2}$ .
Simplify Terms: Simplify each term: $5x + 2(x-1) = \left(\frac{3}{2}\right) \cdot 5(x-1)$ .
Combine Like Terms: Distribute the $2$ and the $(3/2) \times 5$ across the respective parentheses: $\newline$ $5x + 2x - 2 = (\frac{15}{2})(x-1)$ .
Distribute Right Side: Combine like terms on the left side of the equation: $7x - 2 = \left(\frac{15}{2}\right)(x-1)$ .
Clear Fractions: Distribute the $\frac{15}{2}$ on the right side of the equation: $7x - 2 = \frac{15}{2}x - \frac{15}{2}$ .
Simplify Equation: Multiply every term by $2$ to clear the fraction on the right side of the equation: $\newline$ $2(7x) - 2(2) = 2\left(\frac{15}{2}x\right) - 2\left(\frac{15}{2}\right)$ .
Isolate Variable: Simplify the equation: $14x - 4 = 15x - 15$ .
Solve for x: Subtract $14x$ from both sides to get the x terms on one side: $\newline$ $-4 = x - 15$ .
Solve for x: Subtract $14x$ from both sides to get the x terms on one side: $\newline$ $-4 = x - 15$ . Add $15$ to both sides to solve for x: $\newline$ $x = 11$ .