Simplify this rational expression: 5x^2+3x-11/x+3 what is the quotient and remainder

Answer with explanation:

 The given rational expression is:

Use Euclid Division Algorithm to solve this ,which states that, if a and b are two expressions, when a divided by b, gives remainder m and Quotient g, then by the application of Division theorem , it can be written as:

⇒ a = b g +m, where, 0≤m<g

⇒5 x²+3 x-11=(5 x-12)(x+3)+25

Quotient = 5 x -12

Remainder =25

m∠cdf = 43° , m∠gdf = 114°, m∠gde = 23°, m∠edh = 23° , m∠cdh = 157°

step-by-step explanation:

since, it is given that de bisects the angle gdh ⇒ de divides the angle gdh into two equal angles.

⇒ m∠gde = m∠edh

⇒ 8·x   - 1 = 6·x + 5

⇒ x = 3

so, m∠gde = 8·x - 1 = 23°

and m∠edh = 23°

now, it is given ∠cde is an straight angle so, m∠cde = 180°

⇒ m∠cdf + m∠fdg + m∠gde = 180°

⇒ 43° + m∠fdg + 23° = 180°

⇒ m∠fdg = 114°

again, m∠cde = m∠cdh + m∠edh = 180°

m∠cdh + 23° = 180°

⇒ m∠cdh = 157°