Question

$\huge \bf \red{Q} \blue{u} \pink{є} \green{ѕ} \orange{т} \purple{i} \gray{o} \blue{n}$

Solve the following equation.

$\bf\dfrac{10x {}^{2} + 15x + 63}{5x {}^{2} - 25x + 12} = \dfrac{2x + 3}{x - 5}$

Answer 1

Step-by-step explanation:

10x2+15x+63=x−52x+3

=>5x(x−5)+125x(2x+3)+63=x−52x+3

Let, 2x+3=a and x−5=b

=>5xb+125xa+63=ba

=>5xab+63b=5xab+12a

=>63(x−5)=12(2x+3)

=>63x−315=24x+36

=>39x=280

=>x=9

Answer 2

Step-by-step explanation:

Given:

$\bf\dfrac{10x {}^{2} + 15x + 63}{5x {}^{2} - 25x + 12} = \dfrac{2x + 3}{x - 5}$

To find: Solve the equation.

Solution:

Step 1: Cross multiply the terms

$(10x {}^{2} + 15x + 63)(x-5)=(5x {}^{2} - 25x + 12)(2x + 3)$

Step 2: Multiply and open brackets both sides

$10x {}^{3} + 15 {x}^{2} + 63x - 50 {x}^{2} - 75x - 315=10x {}^{3} - 50 {x}^{2} + 24x + 15 {x}^{2} - 75x + 36$

Step 3: Cancel similar terms with same sign both sides

$\cancel{10x {}^{3}} +\cancel{15 {x}^{2}} + 63x -\cancel{50 {x}^{2}} - \cancel{75x} - 315=\cancel{10x {}^{3}} - \cancel{50 {x}^{2}} + 24x + \cancel{15 {x}^{2}} - \cancel{75x} + 36$

Step 4: Add /subtract remaining terms

$63x- 315= 24x + 36 \\ \\ 63x - 24x= 36 + 315 \\ \\ 39x = 351\\\\x=\frac{351}{39}\\\\x=9$

Final answer:

x=9

Hope it helps you.

To learn more on brainly:

Please solve it

https://brainly.in/question/46996785