rational equation

Question

chinTyro

Asked: April 9, 20212021-04-09T15:13:17+00:00 2021-04-09T15:13:17+00:00In: Calculus and Trigonometry, High School/Senior Secondary School

find the solution set of the rational equation

(1/4x+3) + (2/4x+3)= (10/ 2x-5)

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acedstud · Accepted Answer · 2021-04-09T20:46:15+00:00

Best Answer

acedstud

Given $\dfrac{1}{4x+3}+\dfrac{2}{4x+3}=\dfrac{10}{2x-5}$ .

Because the left-hand side of the equation have the same denominator, we can add the numerator and have,

$\dfrac{3}{4x+3}=\dfrac{10}{2x-5}$

Multiplying both sides by the LCD, (4x+3)(2x-5), we have

$(4x+3)(2x-5)\dfrac{3}{4x+3}=(4x+3)(2x-5)\dfrac{10}{2x-5}\Rightarrow3(2x-5)=10(4x+3)$

$\Rightarrow6x-15=40x+30\Rightarrow40x-6x=-15-30\Rightarrow34x=-45\Rightarrow x=-\dfrac{45}{34}$ .

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