Question

14x² - 6x +8 / 10x² + 4x +7 = 7x - 3 / 5x +2​

Answer 1

Answer:

37/9

Step-by-step explanation:

5x+2(14x^2-6x+8)=7x-3(10x^2+4x+7)

37=9x

x=37/9

Answer 2

Correct Question:

Solve the equation $\frac{14x^2 - 6x +8 }{ 10x^2 + 4x +7 }= \frac{7x - 3 }{ 5x +2}$ and find the value of x.

Final Answer:

The value of x obtained by solving the equation $\frac{14x^2 - 6x +8 }{ 10x^2 + 4x +7 }= \frac{7x - 3 }{ 5x +2}$ is $\frac{37}{9}$

Given:

The  equation $\frac{14x^2 - 6x +8 }{ 10x^2 + 4x +7 }= \frac{7x - 3 }{ 5x +2}$ is provided.

To Find:

The value of x obtained by solving the equation $\frac{14x^2 - 6x +8 }{ 10x^2 + 4x +7 }= \frac{7x - 3 }{ 5x +2}$  is to be calculated.

Explanation:

The concepts helpful in figuring out the solution here are as follows.

• The equation $\frac{14x^2 - 6x +8 }{ 10x^2 + 4x +7 }= \frac{7x - 3 }{ 5x +2}$  has two algebraic fractions $\frac{14x^2 - 6x +8 }{ 10x^2 + 4x +7 },\frac{7x - 3 }{ 5x +2}$.
• Any fraction shows two parts, the numerator and the denominator.
• The numerator (x) of the fraction $\frac{x}{y}$ is used to particularly indicate the upper part  of the fraction.
• The denominator (y) of the fraction $\frac{x}{y}$ is used to particularly indicate the lower part of the fraction.

Step 1 of 2

As per the given statement in the problem, cross multiply the numerators and the denominators of the two algebraic fractions $\frac{14x^2 - 6x +8 }{ 10x^2 + 4x +7 },\frac{7x - 3 }{ 5x +2}$ of the equation to get the following.

$(14x^2 - 6x +8 )({ 5x +2})=( 10x^2 + 4x +7 )(7x - 3 )\\5x(14x^2 - 6x +8 )+2(14x^2 - 6x +8 )=7x( 10x^2 + 4x +7 )-3( 10x^2 + 4x +7 )\\70x^3-30x^2+40x+28x^2-12x+16=70x^3+28x^2+49x-30x^2-12x-21$

Step 2 of 2

From the above equation cancel the common terms, and solve it as shown below.

$49x-40x=21+16\\9x=37\\x=\frac{37}{9}$

Therefore, the required correct answer is the value $x=\frac{37}{9}$.

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